<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Simplifying Complex Fractions</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      color: #1e293b;
      background: transparent;
      padding: 12px 8px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100vh;
      max-height: 560px;
    }

    .container {
      width: 100%;
      max-width: 600px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
    }

    /* Header Nav */
    .nav-bar {
      display: flex;
      gap: 6px;
      width: 100%;
      justify-content: center;
      flex-wrap: wrap;
    }

    .nav-btn {
      flex: 1 1 calc(25% - 6px);
      min-width: 75px;
      padding: 8px 6px;
      font-size: 12px;
      font-weight: 600;
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      color: #475569;
      cursor: pointer;
      text-align: center;
      transition: background 0.15s ease, color 0.15s ease, border-color 0.15s ease;
      white-space: nowrap;
    }

    .nav-btn.active {
      background: #0284c7;
      color: #ffffff;
      border-color: #0284c7;
      box-shadow: 0 2px 5px rgba(2, 132, 199, 0.25);
    }

    /* Presentation Area */
    .stage {
      position: relative;
      width: 100%;
      min-height: 250px;
      display: flex;
      align-items: center;
      justify-content: center;
      overflow: hidden;
    }

    .step-panel {
      display: none;
      width: 100%;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      text-align: center;
      gap: 12px;
      animation: fadeIn 0.25s ease-out;
    }

    .step-panel.active {
      display: flex;
    }

    @keyframes fadeIn {
      from { opacity: 0; transform: translateY(4px); }
      to { opacity: 1; transform: translateY(0); }
    }

    .step-badge {
      font-size: 11px;
      font-weight: 700;
      letter-spacing: 0.5px;
      text-transform: uppercase;
      color: #0369a1;
      background: #e0f2fe;
      padding: 4px 12px;
      border-radius: 12px;
      display: inline-block;
    }

    .step-desc {
      font-size: 13px;
      color: #475569;
      max-width: 90%;
      line-height: 1.4;
    }

    /* Math Rendering Engine using pure CSS */
    .math {
      font-family: 'Cambria Math', 'KaTeX_Math', 'STIX Two Math', 'Times New Roman', serif;
      font-size: 20px;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      line-height: 1;
      color: #0f172a;
    }

    .math var {
      font-style: italic;
      font-family: inherit;
    }

    .math sup {
      font-size: 0.7em;
      vertical-align: top;
      position: relative;
      top: -0.4em;
      margin-left: 1px;
    }

    .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      padding: 0 4px;
    }

    .frac > .num {
      border-bottom: 1.5px solid #334155;
      padding-bottom: 2px;
      display: block;
    }

    .frac > .den {
      padding-top: 2px;
      display: block;
    }

    .big-frac {
      font-size: 18px;
    }

    .big-frac > .num {
      border-bottom: 2px solid #0f172a;
      padding: 6px 8px;
    }

    .big-frac > .den {
      padding: 6px 8px;
    }

    .paren-wrap {
      display: inline-flex;
      align-items: center;
    }

    .paren-big {
      font-size: 1.6em;
      font-weight: 300;
      transform: scaleY(1.3);
      color: #475569;
      user-select: none;
    }

    .highlight-lcd {
      color: #0284c7;
      font-weight: bold;
    }

    .highlight-factor {
      color: #0284c7;
      font-weight: 600;
    }

    /* Coral Strike-through */
    .strike-coral {
      position: relative;
      display: inline-flex;
      align-items: center;
      color: #e11d48;
      font-weight: 600;
    }

    .strike-coral::after {
      content: '';
      position: absolute;
      left: -4px;
      right: -4px;
      top: 50%;
      height: 2.5px;
      background: #f43f5e;
      border-radius: 2px;
      transform: rotate(-10deg);
    }

    /* Final Answer Box */
    .final-box {
      background: #f0fdf4;
      border: 2px solid #16a34a;
      padding: 8px 18px;
      border-radius: 8px;
      margin-top: 4px;
      display: inline-flex;
      align-items: center;
      gap: 10px;
    }

    .final-label {
      font-family: system-ui, -apple-system, sans-serif;
      font-size: 12px;
      font-weight: 700;
      color: #15803d;
      text-transform: uppercase;
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 14px;
      width: 100%;
      padding-top: 4px;
    }

    .ctrl-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 6px 14px;
      font-size: 13px;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      gap: 4px;
      transition: background 0.15s ease, border-color 0.15s ease;
    }

    .ctrl-btn:hover {
      background: #f8fafc;
      border-color: #94a3b8;
    }

    .ctrl-btn:active {
      background: #e2e8f0;
    }

    .dots-container {
      display: flex;
      gap: 8px;
      align-items: center;
    }

    .dot {
      width: 9px;
      height: 9px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      transition: background 0.2s ease;
    }

    .dot.active {
      background: #0284c7;
      width: 11px;
      height: 11px;
    }

    @media (max-width: 480px) {
      .math { font-size: 17px; }
      .big-frac { font-size: 15px; }
      .nav-btn { font-size: 11px; padding: 6px 2px; }
      .step-badge { font-size: 10px; }
      .step-desc { font-size: 12px; }
    }
  </style>
</head>
<body>

  <div class="container">
    
    <div class="nav-bar">
      <button class="nav-btn active" data-step="0">1. Multiply LCD</button>
      <button class="nav-btn" data-step="1">2. Distribute</button>
      <button class="nav-btn" data-step="2">3. Factor</button>
      <button class="nav-btn" data-step="3">4. Cancel</button>
    </div>

    
    <div class="stage">
      
      <div class="step-panel active" id="panel-0">
        <span class="step-badge">Step 1: Common Denominator</span>
        <p class="step-desc">Multiply numerator and denominator by the LCD of all inner fractions: <strong class="highlight-lcd"><var>x</var><sup>2</sup><var>y</var><sup>2</sup></strong></p>
        <div class="math">
          <div class="frac big-frac">
            <div class="num">
              <span class="paren-wrap">
                <span class="paren-big">(</span>
                <span class="frac"><span class="num">3</span><span class="den"><var>x</var></span></span>
                &minus;
                <span class="frac"><span class="num">2</span><span class="den"><var>y</var></span></span>
                <span class="paren-big">)</span>
              </span>
              &sdot;
              <span class="highlight-lcd"><var>x</var><sup>2</sup><var>y</var><sup>2</sup></span>
            </div>
            <div class="den">
              <span class="paren-wrap">
                <span class="paren-big">(</span>
                <span class="frac"><span class="num">9</span><span class="den"><var>x</var><sup>2</sup></span></span>
                &minus;
                <span class="frac"><span class="num">4</span><span class="den"><var>y</var><sup>2</sup></span></span>
                <span class="paren-big">)</span>
              </span>
              &sdot;
              <span class="highlight-lcd"><var>x</var><sup>2</sup><var>y</var><sup>2</sup></span>
            </div>
          </div>
        </div>
      </div>

      
      <div class="step-panel" id="panel-1">
        <span class="step-badge">Step 2: Distribute & Clear</span>
        <p class="step-desc">Distribute <strong class="highlight-lcd"><var>x</var><sup>2</sup><var>y</var><sup>2</sup></strong> into each term to eliminate internal fractions:</p>
        <div class="math">
          <div class="frac big-frac">
            <div class="num">
              3<var>x</var><span class="highlight-lcd"><var>y</var><sup>2</sup></span> &minus; 2<span class="highlight-lcd"><var>x</var><sup>2</sup></span><var>y</var>
            </div>
            <div class="den">
              9<span class="highlight-lcd"><var>y</var><sup>2</sup></span> &minus; 4<span class="highlight-lcd"><var>x</var><sup>2</sup></span>
            </div>
          </div>
        </div>
      </div>

      
      <div class="step-panel" id="panel-2">
        <span class="step-badge">Step 3: Factor Terms</span>
        <p class="step-desc">Factor GCF <strong class="highlight-lcd"><var>xy</var></strong> from numerator, and difference of squares from denominator:</p>
        <div class="math">
          <div class="frac big-frac">
            <div class="num">
              <var>x</var><var>y</var>
              <span class="highlight-factor">(3<var>y</var> &minus; 2<var>x</var>)</span>
            </div>
            <div class="den">
              <span class="highlight-factor">(3<var>y</var> &minus; 2<var>x</var>)</span>(3<var>y</var> + 2<var>x</var>)
            </div>
          </div>
        </div>
      </div>

      
      <div class="step-panel" id="panel-3">
        <span class="step-badge">Step 4: Cancel Common Factor</span>
        <p class="step-desc">Cancel the common binomial <strong style="color: #e11d48;">(3<var>y</var> &minus; 2<var>x</var>)</strong> to simplify fully:</p>
        <div class="math" style="margin-bottom: 6px;">
          <div class="frac big-frac">
            <div class="num">
              <var>x</var><var>y</var>
              <span class="strike-coral">(3<var>y</var> &minus; 2<var>x</var>)</span>
            </div>
            <div class="den">
              <span class="strike-coral">(3<var>y</var> &minus; 2<var>x</var>)</span>(3<var>y</var> + 2<var>x</var>)
            </div>
          </div>
        </div>

        <div class="final-box">
          <span class="final-label">Simplified:</span>
          <div class="math" style="font-size: 20px; font-weight: bold;">
            <div class="frac">
              <span class="num"><var>x</var><var>y</var></span>
              <span class="den">3<var>y</var> + 2<var>x</var></span>
            </div>
          </div>
        </div>
      </div>
    </div>

    
    <div class="controls">
      <button class="ctrl-btn" id="prevBtn" aria-label="Previous step">&larr; Prev</button>
      <button class="ctrl-btn" id="playBtn" aria-label="Play or pause auto-advancing">&#10074;&#10074; Pause</button>
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        <div class="dot active" data-step="0" title="Step 1"></div>
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      <button class="ctrl-btn" id="nextBtn" aria-label="Next step">Next &rarr;</button>
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Simplifying Complex Fractions Using LCD Multiplication

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
    }

    body {
      background: transparent;
      color: #0f172a;
      padding: 8px 4px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: flex-start;
      min-height: 100%;
      user-select: none;
    }

    .container {
      width: 100%;
      max-width: 620px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
    }

    /* Navigation & Stepper */
    .nav-bar {
      display: flex;
      align-items: center;
      justify-content: space-between;
      width: 100%;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px 10px;
      gap: 8px;
    }

    .nav-left {
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .step-btn {
      background: #ffffff;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 5px 12px;
      font-size: 12px;
      font-weight: 600;
      color: #334155;
      cursor: pointer;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      transition: background 0.3s ease, border-color 0.3s ease, color 0.3s ease;
    }

    .step-btn:hover {
      background: #f1f5f9;
      border-color: #94a3b8;
      color: #0f172a;
    }

    .step-btn:active {
      background: #e2e8f0;
    }

    .step-indicator {
      font-size: 12px;
      font-weight: 700;
      color: #64748b;
      letter-spacing: 0.3px;
    }

    .dot-track {
      display: flex;
      gap: 6px;
      align-items: center;
    }

    .dot {
      width: 10px;
      height: 10px;
      border-radius: 50%;
      background: #cbd5e1;
      cursor: pointer;
      transition: background 0.3s ease, box-shadow 0.3s ease;
    }

    .dot.active {
      background: #0284c7;
      box-shadow: 0 0 0 3px rgba(2, 132, 199, 0.25);
    }

    /* Content Stage */
    .stage-wrapper {
      position: relative;
      width: 100%;
      min-height: 260px;
      background: transparent;
    }

    .step-card {
      display: none;
      width: 100%;
      padding: 4px 2px;
      flex-direction: column;
      align-items: center;
      text-align: center;
      gap: 12px;
      animation: fadeIn 0.35s ease forwards;
    }

    .step-card.active {
      display: flex;
    }

    @keyframes fadeIn {
      from { opacity: 0; transform: translateY(5px); }
      to { opacity: 1; transform: translateY(0); }
    }

    /* Tags */
    .step-badge {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.6px;
      padding: 4px 10px;
      border-radius: 20px;
    }

    .badge-blue { background: #e0f2fe; color: #0369a1; border: 1px solid #bae6fd; }
    .badge-amber { background: #fef3c7; color: #b45309; border: 1px solid #fde68a; }
    .badge-purple { background: #f3e8ff; color: #7e22ce; border: 1px solid #e9d5ff; }
    .badge-teal { background: #ccfbf1; color: #0f766e; border: 1px solid #99f6e4; }
    .badge-green { background: #dcfce7; color: #15803d; border: 1px solid #bbf7d0; }

    .step-title {
      font-size: 15px;
      font-weight: 700;
      color: #1e293b;
      margin-top: -2px;
    }

    /* Math Typography & Layout */
    .math-canvas {
      width: 100%;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 14px 10px;
      display: flex;
      align-items: center;
      justify-content: center;
      overflow-x: auto;
      min-height: 100px;
    }

    .math-row {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      font-family: "Cambria Math", "KaTeX_Math", "Times New Roman", serif;
      font-size: 18px;
      color: #0f172a;
      gap: 6px;
      white-space: nowrap;
    }

    /* HTML Fraction Builder */
    .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      padding: 0 3px;
    }

    .num {
      border-bottom: 1.5px solid #334155;
      padding: 1px 4px 2px 4px;
      line-height: 1.1;
    }

    .den {
      padding: 2px 4px 1px 4px;
      line-height: 1.1;
    }

    /* Large Outer Complex Fraction */
    .big-frac > .num {
      border-bottom: 2.5px solid #0f172a;
      padding: 6px 8px;
    }

    .big-frac > .den {
      padding: 6px 8px;
    }

    .highlight-lcd {
      color: #0284c7;
      font-weight: 700;
      background: #e0f2fe;
      padding: 2px 4px;
      border-radius: 4px;
      border: 1px dashed #38bdf8;
    }

    .highlight-whole {
      color: #b45309;
      font-weight: 700;
      background: #fef3c7;
      padding: 2px 4px;
      border-radius: 4px;
      border: 1px dashed #f59e0b;
    }

    .highlight-res {
      color: #15803d;
      font-weight: 700;
      background: #dcfce7;
      padding: 3px 8px;
      border-radius: 6px;
    }

    .strike {
      position: relative;
      display: inline-block;
      opacity: 0.65;
    }

    .strike::after {
      content: '';
      position: absolute;
      left: -2px;
      right: -2px;
      top: 50%;
      height: 2px;
      background: #ef4444;
      transform: rotate(-10deg);
      border-radius: 2px;
    }

    /* Explanation note banner */
    .note-box {
      font-size: 13px;
      color: #475569;
      background: #f8fafc;
      border-left: 3px solid #0284c7;
      border-radius: 0 6px 6px 0;
      padding: 8px 12px;
      text-align: left;
      width: 100%;
      line-height: 1.45;
      transition: border-color 0.3s ease, background-color 0.3s ease;
    }

    .note-box strong {
      color: #0f172a;
    }

    .note-box.alert {
      border-left-color: #f59e0b;
      background: #fffbeb;
    }

    /* Responsive styling */
    @media (max-width: 480px) {
      .math-row {
        font-size: 14.5px;
      }
      .step-title {
        font-size: 13.5px;
      }
      .note-box {
        font-size: 12px;
        padding: 6px 10px;
      }
      .nav-bar {
        padding: 5px 8px;
      }
      .step-btn {
        padding: 4px 8px;
        font-size: 11px;
      }
    }
  </style>
</head>
<body>

  <div class="container">
    
    <div class="nav-bar">
      <div class="nav-left">
        <button class="step-btn" id="prevBtn" aria-label="Previous step">◀ Prev</button>
        <button class="step-btn" id="nextBtn" aria-label="Next step">Next ▶</button>
        <button class="step-btn" id="playBtn" aria-label="Auto play/pause" style="min-width: 32px;">⏸</button>
      </div>

      <span class="step-indicator" id="stepCounter">Step 1 of 5</span>

      <div class="dot-track" id="dotTrack">
        <div class="dot active" data-step="0"></div>
        <div class="dot" data-step="1"></div>
        <div class="dot" data-step="2"></div>
        <div class="dot" data-step="3"></div>
        <div class="dot" data-step="4"></div>
      </div>
    </div>

    
    <div class="stage-wrapper">
      
      
      <div class="step-card active" id="card0">
        <span class="step-badge badge-blue">Step 1</span>
        <div class="step-title">Identify the Common Denominator (LCD)</div>
        <div class="math-canvas">
          <div class="math-row">
            <div class="frac big-frac">
              <span class="num">
                <span class="frac"><span class="num">1</span><span class="den">x − 2</span></span> + 3
              </span>
              <span class="den">
                <span class="frac"><span class="num">5</span><span class="den">x² − 4</span></span>
              </span>
            </div>
            <span style="font-size: 20px; margin: 0 8px;">=</span>
            <div class="frac big-frac">
              <span class="num">
                <span class="frac"><span class="num">1</span><span class="den">x − 2</span></span> + 3
              </span>
              <span class="den">
                <span class="frac"><span class="num">5</span><span class="den">(x − 2)(x + 2)</span></span>
              </span>
            </div>
          </div>
        </div>
        <div class="note-box">
          Factor the denominator: <strong>x² − 4 = (x − 2)(x + 2)</strong>.<br>
          The LCD of all internal fractions is <strong style="color:#0284c7;">(x − 2)(x + 2)</strong>.
        </div>
      </div>

      
      <div class="step-card" id="card1">
        <span class="step-badge badge-amber">Step 2</span>
        <div class="step-title">Distribute LCD to Every Single Term</div>
        <div class="math-canvas">
          <div class="math-row">
            <div class="frac big-frac">
              <span class="num">
                <span class="frac"><span class="num">1</span><span class="den">x − 2</span></span><span class="highlight-lcd">(x − 2)(x + 2)</span>
                &nbsp;+&nbsp;
                3<span class="highlight-whole">(x − 2)(x + 2)</span>
              </span>
              <span class="den">
                <span class="frac"><span class="num">5</span><span class="den">(x − 2)(x + 2)</span></span><span class="highlight-lcd">(x − 2)(x + 2)</span>
              </span>
            </div>
          </div>
        </div>
        <div class="note-box alert">
          <strong>Key Rule:</strong> The whole number <strong>3</strong> must also be multiplied by the full LCD <strong style="color:#b45309;">(x − 2)(x + 2) = (x² − 4)</strong>!
        </div>
      </div>

      
      <div class="step-card" id="card2">
        <span class="step-badge badge-purple">Step 3</span>
        <div class="step-title">Cancel Denominators to Clear Fractions</div>
        <div class="math-canvas">
          <div class="math-row">
            <div class="frac big-frac">
              <span class="num">
                <span class="frac"><span class="num">1</span><span class="den strike">x − 2</span></span><span class="strike highlight-lcd">(x − 2)</span>(x + 2)
                &nbsp;+&nbsp;
                3<span class="highlight-whole">(x² − 4)</span>
              </span>
              <span class="den">
                <span class="frac"><span class="num">5</span><span class="den strike">(x − 2)(x + 2)</span></span><span class="strike highlight-lcd">(x − 2)(x + 2)</span>
              </span>
            </div>
            <span style="font-size: 20px; margin: 0 8px;">⟹</span>
            <div class="frac">
              <span class="num">(x + 2) + 3(x² − 4)</span>
              <span class="den">5</span>
            </div>
          </div>
        </div>
        <div class="note-box">
          Denominator simplifies to <strong>5</strong>. The numerator becomes <strong>(x + 2) + 3(x² − 4)</strong>.
        </div>
      </div>

      
      <div class="step-card" id="card3">
        <span class="step-badge badge-teal">Step 4</span>
        <div class="step-title">Expand and Combine Like Terms</div>
        <div class="math-canvas">
          <div class="math-row">
            <div class="frac">
              <span class="num">x + 2 + 3x² − 12</span>
              <span class="den">5</span>
            </div>
            <span style="font-size: 20px; margin: 0 8px;">=</span>
            <div class="frac">
              <span class="num">3x² + x − 10</span>
              <span class="den">5</span>
            </div>
          </div>
        </div>
        <div class="note-box">
          Distribute 3: <strong>3 · x² − 3 · 4 = 3x² − 12</strong>.<br>
          Combine constants: <strong>2 − 12 = −10</strong>, giving <strong>3x² + x − 10</strong> in the numerator.
        </div>
      </div>

      
      <div class="step-card" id="card4">
        <span class="step-badge badge-green">Step 5</span>
        <div class="step-title">Factor Numerator for Final Answer</div>
        <div class="math-canvas">
          <div class="math-row">
            <div class="frac highlight-res">
              <span class="num" style="border-bottom: 2px solid #15803d; font-size: 19px;">(3x − 5)(x + 2)</span>
              <span class="den" style="font-size: 19px;">5</span>
            </div>
          </div>
        </div>
        <div class="note-box">
          Factor 3x² + x − 10 into <strong>(3x − 5)(x + 2)</strong>.<br>
          Since no terms cancel with the denominator 5, this is the fully simplified form.
        </div>
      </div>

    </div>
  </div>

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</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      background: transparent;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      gap: 12px;
    }

    /* Top Segmented Controls */
    .controls {
      display: flex;
      background: #f1f5f9;
      padding: 3px;
      border-radius: 999px;
      gap: 2px;
      width: 100%;
      max-width: 480px;
    }

    .pill-btn {
      flex: 1;
      padding: 6px 10px;
      border: none;
      background: transparent;
      color: #64748b;
      font-size: 13px;
      font-weight: 600;
      border-radius: 999px;
      cursor: pointer;
      transition: all 0.25s ease;
      white-space: nowrap;
      text-align: center;
    }

    .pill-btn.active {
      background: #ffffff;
      color: #0284c7;
      box-shadow: 0 1px 3px rgba(0, 0, 0, 0.1);
    }

    /* Fraction Workspace Layout */
    .stage-wrapper {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 16px;
      width: 100%;
      max-width: 500px;
      flex: 1;
      min-height: 220px;
    }

    .fraction-column {
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      width: 200px;
    }

    .math-text {
      font-family: 'KaTeX_Math', 'Cambria Math', 'Times New Roman', serif;
      font-style: italic;
      font-size: 26px;
      user-select: none;
    }

    .math-op {
      font-family: system-ui, sans-serif;
      font-style: normal;
      font-weight: 500;
      margin: 0 6px;
      font-size: 20px;
      color: #475569;
    }

    /* Overall Numerator & Denominator Blocks */
    .num-block, .den-block {
      display: flex;
      align-items: center;
      justify-content: center;
      padding: 10px 18px;
      border-radius: 12px;
      border: 2px solid transparent;
      transition: all 0.3s ease;
      width: 100%;
    }

    .num-block {
      background: #e0f2fe;
      border-color: #38bdf8;
      color: #0369a1;
    }

    .den-block {
      background: #fef3c7;
      border-color: #f59e0b;
      color: #92400e;
    }

    /* Mini Fractions */
    .mini-frac {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      vertical-align: middle;
      line-height: 1;
      padding: 2px 4px;
    }

    .mini-bar {
      width: 100%;
      height: 2px;
      background: currentColor;
      border-radius: 1px;
      margin: 3px 0;
      opacity: 0.8;
    }

    /* Inner Denominators */
    .inner-den {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      padding: 1px 7px;
      border-radius: 6px;
      background: #fee2e2;
      border: 1.5px solid #ef4444;
      color: #b91c1c;
      font-weight: bold;
      transition: all 0.3s ease;
    }

    /* Main Fraction Bar */
    .main-bar-container {
      width: 100%;
      padding: 6px 0;
      position: relative;
    }

    .main-bar {
      width: 100%;
      height: 4px;
      background: #0284c7;
      border-radius: 999px;
      transition: all 0.3s ease;
    }

    /* Callout Pointers Panel */
    .callouts {
      display: flex;
      flex-direction: column;
      justify-content: space-between;
      height: 190px;
      gap: 8px;
    }

    .callout-item {
      display: flex;
      align-items: center;
      gap: 6px;
      font-size: 12px;
      font-weight: 700;
      padding: 6px 10px;
      border-radius: 8px;
      transition: all 0.3s ease;
      white-space: nowrap;
    }

    .callout-num {
      background: #e0f2fe;
      color: #0369a1;
      border: 1px solid #bae6fd;
    }

    .callout-bar {
      background: #f0f9ff;
      color: #0284c7;
      border: 1px solid #7dd3fc;
    }

    .callout-den {
      background: #fef3c7;
      color: #92400e;
      border: 1px solid #fde68a;
    }

    .callout-lcd {
      background: #fee2e2;
      color: #b91c1c;
      border: 1px solid #fca5a5;
    }

    .arrow {
      font-style: normal;
      font-weight: normal;
    }

    /* Mode Dynamic States */
    /* Mode 2: Outer Structure Focus */
    body[data-mode="2"] .mini-frac {
      opacity: 0.45;
    }
    body[data-mode="2"] .inner-den {
      background: transparent;
      border-color: transparent;
      color: inherit;
    }
    body[data-mode="2"] .callout-lcd {
      opacity: 0.3;
    }

    /* Mode 3: Inner LCD Targets Focus */
    body[data-mode="3"] .num-block {
      background: rgba(224, 242, 254, 0.4);
      border-color: rgba(56, 189, 248, 0.3);
      color: #64748b;
    }
    body[data-mode="3"] .den-block {
      background: rgba(254, 243, 199, 0.4);
      border-color: rgba(245, 158, 11, 0.3);
      color: #64748b;
    }
    body[data-mode="3"] .main-bar {
      opacity: 0.3;
    }
    body[data-mode="3"] .inner-den {
      background: #fee2e2;
      border-color: #ef4444;
      color: #b91c1c;
      box-shadow: 0 0 0 3px rgba(239, 68, 68, 0.25);
      animation: pulse-ring 1.8s infinite ease-in-out;
    }
    body[data-mode="3"] .callout-num,
    body[data-mode="3"] .callout-bar,
    body[data-mode="3"] .callout-den {
      opacity: 0.3;
    }

    @keyframes pulse-ring {
      0%, 100% { box-shadow: 0 0 0 2px rgba(239, 68, 68, 0.3); }
      50% { box-shadow: 0 0 0 5px rgba(239, 68, 68, 0.6); }
    }

    /* Explanatory Footer */
    .footer-box {
      width: 100%;
      max-width: 480px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 8px 14px;
      display: flex;
      align-items: center;
      justify-content: center;
      min-height: 42px;
      text-align: center;
    }

    .footer-text {
      font-size: 13px;
      color: #334155;
      font-weight: 500;
    }

    .footer-text b {
      color: #0f172a;
    }

    @media (max-width: 420px) {
      .controls {
        font-size: 11px;
      }
      .pill-btn {
        font-size: 11px;
        padding: 5px 6px;
      }
      .stage-wrapper {
        gap: 8px;
      }
      .fraction-column {
        width: 160px;
      }
      .math-text {
        font-size: 22px;
      }
      .callout-item {
        font-size: 10px;
        padding: 4px 6px;
      }
    }
  </style>
</head>
<body data-mode="1">

  
  <div class="controls" role="tablist">
    <button class="pill-btn active" id="btn-1" onclick="setMode(1)">1. Full Anatomy</button>
    <button class="pill-btn" id="btn-2" onclick="setMode(2)">2. Outer View</button>
    <button class="pill-btn" id="btn-3" onclick="setMode(3)">3. LCD Targets</button>
  </div>

  
  <div class="stage-wrapper">
    <div class="fraction-column">
      
      
      <div class="num-block">
        <span class="math-text">
          <span class="mini-frac">
            <span>a</span>
            <span class="mini-bar"></span>
            <span class="inner-den">b</span>
          </span>
          <span class="math-op">+</span>
          <span>c</span>
        </span>
      </div>

      
      <div class="main-bar-container">
        <div class="main-bar"></div>
      </div>

      
      <div class="den-block">
        <span class="math-text">
          <span class="mini-frac">
            <span>d</span>
            <span class="mini-bar"></span>
            <span class="inner-den">e</span>
          </span>
          <span class="math-op">−</span>
          <span>f</span>
        </span>
      </div>

    </div>

    
    <div class="callouts">
      <div class="callout-item callout-num">
        <span class="arrow">←</span> Overall Numerator
      </div>
      <div class="callout-item callout-bar">
        <span class="arrow">←</span> Main Bar (÷)
      </div>
      <div class="callout-item callout-lcd">
        <span class="arrow">←</span> Inner Denominators
      </div>
      <div class="callout-item callout-den">
        <span class="arrow">←</span> Overall Denominator
      </div>
    </div>
  </div>

  
  <div class="footer-box">
    <div class="footer-text" id="caption">
      Fractions nested inside the numerator and denominator.
    </div>
  </div>

  <script>
    const captions = {
      1: "Fractions nested inside the numerator and denominator.",
      2: "Outer view represents <b>(Numerator) ÷ (Denominator)</b>.",
      3: "Multiply top & bottom by <b>LCD(b, e)</b> to clear fractions."
    };

    function setMode(modeNum) {
      document.body.setAttribute('data-mode', modeNum);
      
      // Update buttons
      for (let i = 1; i <= 3; i++) {
        const btn = document.getElementById('btn-' + i);
        if (i === modeNum) {
          btn.classList.add('active');
        } else {
          btn.classList.remove('active');
        }
      }

      // Update caption
      document.getElementById('caption').innerHTML = captions[modeNum];
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Simplifying Complex Fractions</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
      padding: 12px;
      user-select: none;
    }

    /* Stepper Tabs */
    .steps-nav {
      display: flex;
      gap: 6px;
      width: 100%;
      max-width: 480px;
      justify-content: center;
    }
    .step-pill {
      flex: 1;
      text-align: center;
      padding: 6px 4px;
      font-size: 13px;
      font-weight: 600;
      border-radius: 6px;
      background: #f1f5f9;
      color: #64748b;
      cursor: pointer;
      border: none;
      transition: all 0.2s ease;
    }
    .step-pill.active {
      background: #22b7ff;
      color: #ffffff;
    }

    /* Stage Area */
    .stage {
      position: relative;
      width: 100%;
      max-width: 520px;
      height: 250px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .step-card {
      position: absolute;
      inset: 0;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      opacity: 0;
      pointer-events: none;
      transition: opacity 0.3s ease;
    }
    .step-card.active {
      opacity: 1;
      pointer-events: auto;
    }

    /* Math Elements */
    .math-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      font-size: 22px;
      font-weight: 500;
    }
    .frac {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      vertical-align: middle;
      padding: 0 4px;
    }
    .num, .den {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
      padding: 2px 4px;
    }
    .bar {
      width: 100%;
      height: 2px;
      background: #1e2945;
      border-radius: 2px;
    }
    .main-bar {
      height: 3px;
      background: #1e2945;
    }

    /* Inner Small Fractions */
    .mini-frac {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      font-size: 17px;
      vertical-align: middle;
    }
    .mini-frac .bar {
      height: 1.5px;
      background: #1e2945;
    }

    /* Highlights & Badges */
    .highlight-lcd {
      color: #16a34a;
      font-weight: 700;
    }
    .badge {
      display: inline-flex;
      align-items: center;
      gap: 6px;
      padding: 4px 10px;
      font-size: 13px;
      font-weight: 600;
      border-radius: 20px;
      margin-top: 14px;
    }
    .badge-blue {
      background: #e0f2fe;
      color: #0369a1;
    }
    .badge-green {
      background: #dcfce7;
      color: #15803d;
    }

    .bracket {
      font-size: 52px;
      font-weight: 300;
      color: #64748b;
      line-height: 1;
    }

    /* Cancellation & Arrows */
    .term-box {
      display: inline-flex;
      align-items: center;
      position: relative;
      padding: 2px;
    }
    .strike {
      position: relative;
      display: inline-block;
    }
    .strike::after {
      content: "";
      position: absolute;
      left: -2px;
      top: 50%;
      width: calc(100% + 4px);
      height: 2px;
      background: #16a34a;
      transform: rotate(-45deg);
      border-radius: 1px;
    }

    .dist-arrow {
      position: absolute;
      top: -22px;
      left: 50%;
      transform: translateX(-50%);
      font-size: 14px;
      color: #16a34a;
      animation: bounce 1.5s infinite;
    }
    @keyframes bounce {
      0%, 100% { transform: translate(-50%, 0); }
      50% { transform: translate(-50%, -3px); }
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      width: 100%;
      max-width: 480px;
    }
    .btn {
      background: #f1f5f9;
      border: none;
      color: #334155;
      font-size: 14px;
      font-weight: 600;
      padding: 6px 14px;
      border-radius: 6px;
      cursor: pointer;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
    }
    .btn:active {
      background: #e2e8f0;
    }
  </style>
</head>
<body>

  
  <div class="steps-nav">
    <button class="step-pill active" onclick="goToStep(0)">1. Identify</button>
    <button class="step-pill" onclick="goToStep(1)">2. Multiply</button>
    <button class="step-pill" onclick="goToStep(2)">3. Cancel</button>
    <button class="step-pill" onclick="goToStep(3)">4. Result</button>
  </div>

  
  <div class="stage">

    
    <div class="step-card active" id="card-0">
      <div class="math-row">
        <div class="frac">
          <div class="num">
            <div class="mini-frac">
              <span>3</span>
              <div class="bar"></div>
              <span class="highlight-lcd">x</span>
            </div>
            <span>+</span>
            <span>2</span>
          </div>
          <div class="bar main-bar"></div>
          <div class="den">
            <div class="mini-frac">
              <span>1</span>
              <div class="bar"></div>
              <span class="highlight-lcd">x</span>
            </div>
            <span>−</span>
            <span>4</span>
          </div>
        </div>
      </div>
      <div class="badge badge-blue">
        <span>LCD = <b class="highlight-lcd">x</b></span>
      </div>
    </div>

    
    <div class="step-card" id="card-1">
      <div class="math-row">
        <span class="bracket">[</span>
        <div class="frac">
          <div class="num">
            <div class="mini-frac"><span>3</span><div class="bar"></div><span>x</span></div>
            <span>+</span>
            <span>2</span>
          </div>
          <div class="bar main-bar"></div>
          <div class="den">
            <div class="mini-frac"><span>1</span><div class="bar"></div><span>x</span></div>
            <span>−</span>
            <span>4</span>
          </div>
        </div>
        <span class="bracket">]</span>
        <span style="color:#64748b; font-size:18px;">•</span>
        <div class="frac" style="font-weight:700; color:#16a34a;">
          <div class="num">x</div>
          <div class="bar" style="background:#16a34a; height:2.5px;"></div>
          <div class="den">x</div>
        </div>
      </div>
      <div class="badge badge-green">
        <span><b class="highlight-lcd">LCD / LCD</b> = 1</span>
      </div>
    </div>

    
    <div class="step-card" id="card-2">
      <div class="math-row" style="font-size: 19px;">
        <div class="frac">
          
          <div class="num">
            <span class="term-box">
              <span class="highlight-lcd strike">x</span>•<div class="mini-frac"><span>3</span><div class="bar"></div><span class="highlight-lcd strike">x</span></div>
            </span>
            <span>+</span>
            <span class="term-box">
              <span class="highlight-lcd">x</span>•<span>2</span>
            </span>
          </div>
          <div class="bar main-bar"></div>
          
          <div class="den">
            <span class="term-box">
              <span class="highlight-lcd strike">x</span>•<div class="mini-frac"><span>1</span><div class="bar"></div><span class="highlight-lcd strike">x</span></div>
            </span>
            <span>−</span>
            <span class="term-box">
              <span class="highlight-lcd">x</span>•<span>4</span>
            </span>
          </div>
        </div>
      </div>
      <div class="badge badge-green">
        <span>Denominators Cancel ➔</span>
      </div>
    </div>

    
    <div class="step-card" id="card-3">
      <div class="math-row" style="font-size: 26px;">
        <div class="frac">
          <div class="num">3 + 2x</div>
          <div class="bar main-bar"></div>
          <div class="den">1 − 4x</div>
        </div>
      </div>
      <div class="badge badge-green">
        <span>Standard Fraction ✓</span>
      </div>
    </div>

  </div>

  
  <div class="controls">
    <button class="btn" onclick="prevStep()">◀</button>
    <button class="btn" id="playBtn" onclick="togglePlay()">⏸ Pause</button>
    <button class="btn" onclick="nextStep()">▶</button>
  </div>

  <script>
    let currentStep = 0;
    const totalSteps = 4;
    let isPlaying = true;
    let timer = null;

    const cards = [
      document.getElementById('card-0'),
      document.getElementById('card-1'),
      document.getElementById('card-2'),
      document.getElementById('card-3')
    ];
    const pills = document.querySelectorAll('.step-pill');
    const playBtn = document.getElementById('playBtn');

    function updateView() {
      cards.forEach((card, i) => card.classList.toggle('active', i === currentStep));
      pills.forEach((pill, i) => pill.classList.toggle('active', i === currentStep));
    }

    function goToStep(idx) {
      currentStep = (idx + totalSteps) % totalSteps;
      updateView();
    }

    function nextStep() {
      goToStep(currentStep + 1);
    }

    function prevStep() {
      goToStep(currentStep - 1);
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      playBtn.textContent = isPlaying ? '⏸ Pause' : '▶ Play';
      if (isPlaying) startTimer();
      else clearInterval(timer);
    }

    function startTimer() {
      clearInterval(timer);
      timer = setInterval(() => {
        if (isPlaying) nextStep();
      }, 3500);
    }

    startTimer();
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <link rel="stylesheet" href="{{VENDOR_CDN}}/katex.min.css">
  <script src="{{VENDOR_CDN}}/katex.min.js"></script>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, 'Segoe UI', Roboto, sans-serif;
      color: #1e2945;
      background: transparent;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: flex-start;
      user-select: none;
    }

    .main-wrap {
      width: 100%;
      max-width: 460px;
      display: flex;
      flex-direction: column;
      gap: 10px;
    }

    /* Expression Header */
    .expr-card {
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      justify-content: space-between;
      background: #f8fafc;
      border-radius: 10px;
      padding: 8px 14px;
      gap: 8px;
      border: 1px solid #cbd5e1;
    }

    .expr-box {
      font-size: 1.1rem;
      color: #1e2945;
      display: flex;
      align-items: center;
    }

    .expr-tag {
      font-size: 11px;
      font-weight: 700;
      color: #b91c1c;
      background: #fee2e2;
      border: 1px solid #fca5a5;
      padding: 4px 8px;
      border-radius: 6px;
      letter-spacing: 0.3px;
      white-space: nowrap;
    }

    /* Steps List */
    .steps-container {
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .step-row {
      display: flex;
      align-items: center;
      gap: 10px;
      background: #f8fafc;
      border-radius: 10px;
      padding: 8px 12px;
      border: 1.5px solid #cbd5e1;
      transition: border-color 0.2s, background-color 0.2s, box-shadow 0.2s;
    }

    .step-row.inactive {
      background: #f8fafc;
      border-color: #e2e8f0;
      opacity: 0.85;
    }

    .step-row.active {
      opacity: 1;
      border-color: #4361ee;
      background: #ffffff;
      box-shadow: 0 3px 10px rgba(67, 97, 238, 0.12);
    }

    .step-row.completed {
      opacity: 1;
      border-color: #94a3b8;
      background: #ffffff;
    }

    .step-num {
      width: 26px;
      height: 26px;
      border-radius: 50%;
      background: #64748b;
      color: #ffffff;
      font-size: 13px;
      font-weight: 700;
      display: flex;
      align-items: center;
      justify-content: center;
      flex-shrink: 0;
      transition: background-color 0.2s;
    }

    .step-row.active .step-num,
    .step-row.completed .step-num {
      background: #4361ee;
    }

    .step-content {
      display: flex;
      flex-direction: column;
      gap: 2px;
      flex-grow: 1;
      min-width: 0;
    }

    .step-label {
      font-size: 11px;
      font-weight: 700;
      color: #475569;
      text-transform: uppercase;
      letter-spacing: 0.4px;
    }

    .step-row.active .step-label {
      color: #4361ee;
    }

    .step-math {
      font-size: 1rem;
      color: #1e2945;
      overflow-x: auto;
      overflow-y: hidden;
      white-space: nowrap;
    }

    /* Excluded Values Banner */
    .banner {
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      justify-content: center;
      gap: 6px 10px;
      background: #eff6ff;
      border: 2px solid #3b82f6;
      border-radius: 10px;
      padding: 8px 12px;
      font-weight: 700;
      font-size: 13.5px;
      color: #1e2945;
      text-align: center;
      transition: all 0.25s ease;
    }

    .banner.highlighted {
      background: #eef2ff;
      border-color: #4361ee;
      box-shadow: 0 2px 8px rgba(67, 97, 238, 0.15);
    }

    .banner-title {
      color: #1e2945;
    }

    .banner-highlight {
      color: #e11d48;
      font-weight: 800;
      font-size: 1.05rem;
    }

    /* Controls */
    .controls {
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      justify-content: center;
      gap: 6px;
      margin-top: 2px;
    }

    .btn-step {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #1e2945;
      font-size: 12px;
      font-weight: 600;
      padding: 6px 10px;
      border-radius: 6px;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 4px;
      transition: background-color 0.15s, border-color 0.15s;
    }

    .btn-step:hover {
      background: #e2e8f0;
      border-color: #94a3b8;
    }

    .btn-step.active {
      background: #4361ee;
      color: #ffffff;
      border-color: #4361ee;
    }

    @media (max-width: 380px) {
      .expr-card {
        justify-content: center;
      }
      .btn-step {
        padding: 5px 8px;
        font-size: 11px;
      }
    }
  </style>
</head>
<body>

  <div class="main-wrap">
    
    <div class="expr-card">
      <div id="math-expr" class="expr-box"></div>
      <div class="expr-tag">Set Denominator = 0</div>
    </div>

    
    <div class="steps-container">
      <div class="step-row" id="row-0">
        <div class="step-num">1</div>
        <div class="step-content">
          <div class="step-label">Isolate Denominator</div>
          <div class="step-math" id="math-step-1"></div>
        </div>
      </div>

      <div class="step-row" id="row-1">
        <div class="step-num">2</div>
        <div class="step-content">
          <div class="step-label">Factor Quadratic</div>
          <div class="step-math" id="math-step-2"></div>
        </div>
      </div>

      <div class="step-row" id="row-2">
        <div class="step-num">3</div>
        <div class="step-content">
          <div class="step-label">Solve Each Factor</div>
          <div class="step-math" id="math-step-3"></div>
        </div>
      </div>
    </div>

    
    <div class="banner" id="result-banner">
      <span class="banner-title">Excluded Values:</span>
      <span class="banner-highlight" id="math-banner"></span>
    </div>

    
    <div class="controls">
      <button class="btn-step" id="btn-0" onclick="setStep(0)">1. Denominator</button>
      <button class="btn-step" id="btn-1" onclick="setStep(1)">2. Factor</button>
      <button class="btn-step" id="btn-2" onclick="setStep(2)">3. Solve</button>
      <button class="btn-step" id="btn-all" onclick="setStep(3)">All Steps</button>
    </div>
  </div>

  <script>
    function renderMath() {
      if (typeof katex !== 'undefined') {
        katex.render("\\frac{x + 4}{x^2 - 5x + 6}", document.getElementById('math-expr'), { throwOnError: false });
        katex.render("x^2 - 5x + 6 = 0", document.getElementById('math-step-1'), { throwOnError: false });
        katex.render("(x - 2)(x - 3) = 0", document.getElementById('math-step-2'), { throwOnError: false });
        katex.render("x = 2 \\quad\\text{and}\\quad x = 3", document.getElementById('math-step-3'), { throwOnError: false });
        katex.render("x = 2,\\; 3", document.getElementById('math-banner'), { throwOnError: false });
      } else {
        document.getElementById('math-expr').innerText = '(x + 4)/(x² - 5x + 6)';
        document.getElementById('math-step-1').innerText = 'x² - 5x + 6 = 0';
        document.getElementById('math-step-2').innerText = '(x - 2)(x - 3) = 0';
        document.getElementById('math-step-3').innerText = 'x = 2 and x = 3';
        document.getElementById('math-banner').innerText = 'x = 2, 3';
      }
    }

    let currentStep = 3;
    let timer = null;

    function updateView() {
      for (let i = 0; i < 3; i++) {
        const row = document.getElementById(`row-${i}`);
        const btn = document.getElementById(`btn-${i}`);
        
        row.classList.remove('active', 'completed', 'inactive');
        btn.classList.remove('active');

        if (currentStep === 3) {
          row.classList.add('completed');
        } else if (i === currentStep) {
          row.classList.add('active');
          btn.classList.add('active');
        } else if (i < currentStep) {
          row.classList.add('completed');
        } else {
          row.classList.add('inactive');
        }
      }

      const btnAll = document.getElementById('btn-all');
      const banner = document.getElementById('result-banner');

      if (currentStep === 2 || currentStep === 3) {
        banner.classList.add('highlighted');
      } else {
        banner.classList.remove('highlighted');
      }

      if (currentStep === 3) {
        btnAll.classList.add('active');
      } else {
        btnAll.classList.remove('active');
      }
    }

    function setStep(step) {
      if (timer) clearInterval(timer);
      currentStep = step;
      updateView();
    }

    window.addEventListener('DOMContentLoaded', () => {
      renderMath();
      updateView();
    });
  </script>
</body>
</html>

Simplifying Rational Expressions and Domain Restrictions

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <title>Domain Restrictions Diagram</title>
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }
    body {
      width: 100%;
      min-height: 100%;
      background: #ffffff;
      font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      color: #1e2945;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      padding: 12px;
      gap: 14px;
    }

    .controls {
      display: flex;
      flex-wrap: wrap;
      justify-content: center;
      gap: 8px;
      width: 100%;
      max-width: 580px;
    }
    .btn {
      appearance: none;
      border: 1.5px solid #e2e8f0;
      background: #f8fafc;
      color: #475569;
      padding: 6px 12px;
      border-radius: 20px;
      font-size: 13px;
      font-weight: 600;
      cursor: pointer;
      transition: background 0.2s, color 0.2s, border-color 0.2s, box-shadow 0.2s;
    }
    .btn:hover {
      background: #f1f5f9;
      border-color: #cbd5e1;
    }
    .btn.active {
      background: #0284c7;
      color: #ffffff;
      border-color: #0284c7;
      box-shadow: 0 2px 6px rgba(2, 132, 199, 0.35);
    }
    .btn.active-hole {
      background: #e11d48;
      color: #ffffff;
      border-color: #e11d48;
      box-shadow: 0 2px 6px rgba(225, 29, 72, 0.35);
    }

    .visual-stack {
      width: 100%;
      max-width: 600px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }

    /* SVG Number Line */
    .svg-container {
      width: 100%;
      background: #f8fafc;
      border-radius: 12px;
      border: 1px solid #e2e8f0;
      padding: 6px 0;
    }
    svg {
      width: 100%;
      height: auto;
      display: block;
    }

    /* Notation Cards */
    .notation-card {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px 14px;
      display: flex;
      flex-direction: column;
      gap: 4px;
    }
    .notation-label {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.05em;
      color: #64748b;
    }
    .notation-content {
      font-family: "Cambria Math", "KaTeX_Math", "Times New Roman", serif;
      font-size: 19px;
      display: flex;
      align-items: center;
      justify-content: center;
      flex-wrap: wrap;
      gap: 4px;
      letter-spacing: 0.02em;
    }

    /* Highlights */
    .seg-left, .seg-mid, .seg-right, .hole-neg3, .hole-pos3 {
      transition: opacity 0.25s, transform 0.25s, filter 0.25s;
    }

    .h-seg {
      color: #0284c7;
      font-weight: 700;
      padding: 2px 4px;
      border-radius: 4px;
      transition: background 0.2s, box-shadow 0.2s;
    }
    .h-hole {
      color: #e11d48;
      font-weight: 700;
      padding: 2px 4px;
      border-radius: 4px;
      transition: background 0.2s, box-shadow 0.2s;
    }
    .h-union {
      color: #64748b;
      font-weight: 600;
      padding: 0 2px;
    }
    .dimmed {
      opacity: 0.25 !important;
    }
    .focused {
      opacity: 1 !important;
      background: #fef2f2;
      box-shadow: 0 0 0 2px #fecdd3;
    }
    .focused-blue {
      opacity: 1 !important;
      background: #e0f2fe;
      box-shadow: 0 0 0 2px #bae6fd;
    }
  </style>
</head>
<body>

  
  <div class="controls">
    <button class="btn active" id="btn-all" onclick="setMode('all')">All Valid Numbers</button>
    <button class="btn" id="btn-neg3" onclick="setMode('neg3')">Hole: x ≠ −3</button>
    <button class="btn" id="btn-pos3" onclick="setMode('pos3')">Hole: x ≠ 3</button>
  </div>

  <div class="visual-stack">
    
    <div class="svg-container">
      <svg viewBox="0 0 600 100" xmlns="http://www.w3.org/2000/svg">
        <defs>
          <marker id="arrow-left-base" viewBox="0 0 10 10" refX="1" refY="5" markerWidth="6" markerHeight="6" orient="auto">
            <path d="M 9 1 L 1 5 L 9 9 z" fill="#94a3b8"/>
          </marker>
          <marker id="arrow-right-base" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="6" markerHeight="6" orient="auto">
            <path d="M 1 1 L 9 5 L 1 9 z" fill="#94a3b8"/>
          </marker>
          <marker id="arrow-left-blue" viewBox="0 0 10 10" refX="1" refY="5" markerWidth="7" markerHeight="7" orient="auto">
            <path d="M 9 1 L 1 5 L 9 9 z" fill="#0284c7"/>
          </marker>
          <marker id="arrow-right-blue" viewBox="0 0 10 10" refX="9" refY="5" markerWidth="7" markerHeight="7" orient="auto">
            <path d="M 1 1 L 9 5 L 1 9 z" fill="#0284c7"/>
          </marker>
        </defs>

        
        <line x1="30" y1="45" x2="570" y2="45" stroke="#cbd5e1" stroke-width="3" marker-start="url(#arrow-left-base)" marker-end="url(#arrow-right-base)"/>

        
        
        <g stroke="#94a3b8" stroke-width="1.5">
          <line x1="100" y1="40" x2="100" y2="50"/>
          <line x1="140" y1="40" x2="140" y2="50"/>
          <line x1="180" y1="38" x2="180" y2="52"/>
          <line x1="220" y1="40" x2="220" y2="50"/>
          <line x1="260" y1="40" x2="260" y2="50"/>
          <line x1="300" y1="36" x2="300" y2="54" stroke="#64748b" stroke-width="2"/>
          <line x1="340" y1="40" x2="340" y2="50"/>
          <line x1="380" y1="40" x2="380" y2="50"/>
          <line x1="420" y1="38" x2="420" y2="52"/>
          <line x1="460" y1="40" x2="460" y2="50"/>
          <line x1="500" y1="40" x2="500" y2="50"/>
        </g>

        
        <g font-size="12" font-weight="500" fill="#64748b" text-anchor="middle" font-family="system-ui, sans-serif">
          <text x="180" y="70" font-weight="700" fill="#e11d48">−3</text>
          <text x="300" y="70">0</text>
          <text x="420" y="70" font-weight="700" fill="#e11d48">3</text>
          <text x="18" y="49" font-size="14" fill="#64748b">−∞</text>
          <text x="582" y="49" font-size="14" fill="#64748b">+∞</text>
        </g>

        
        
        <line class="seg-left" x1="172" y1="45" x2="28" y2="45" stroke="#0284c7" stroke-width="6" stroke-linecap="round" marker-end="url(#arrow-left-blue)"/>
        
        
        <line class="seg-mid" x1="188" y1="45" x2="412" y2="45" stroke="#0284c7" stroke-width="6"/>

        
        <line class="seg-right" x1="428" y1="45" x2="572" y2="45" stroke="#0284c7" stroke-width="6" stroke-linecap="round" marker-end="url(#arrow-right-blue)"/>

        
        <g class="hole-neg3">
          <circle cx="180" cy="45" r="7" fill="#ffffff" stroke="#e11d48" stroke-width="3.5"/>
        </g>
        <g class="hole-pos3">
          <circle cx="420" cy="45" r="7" fill="#ffffff" stroke="#e11d48" stroke-width="3.5"/>
        </g>
      </svg>
    </div>

    
    <div class="notation-card">
      <span class="notation-label">Interval Notation</span>
      <div class="notation-content">
        <span class="h-seg seg-left">(−∞, <span class="hole-neg3" style="color:#e11d48">−3</span>)</span>
        <span class="h-union">∪</span>
        <span class="h-seg seg-mid">(<span class="hole-neg3" style="color:#e11d48">−3</span>, <span class="hole-pos3" style="color:#e11d48">3</span>)</span>
        <span class="h-union">∪</span>
        <span class="h-seg seg-right">(<span class="hole-pos3" style="color:#e11d48">3</span>, ∞)</span>
      </div>
    </div>

    
    <div class="notation-card">
      <span class="notation-label">Set-Builder Notation</span>
      <div class="notation-content">
        <span>{</span>
        <span class="h-seg">x ∈ ℝ</span>
        <span style="color:#94a3b8; padding: 0 4px;">|</span>
        <span class="h-hole hole-neg3">x ≠ −3</span>
        <span style="color:#94a3b8">,</span>
        <span class="h-hole hole-pos3">x ≠ 3</span>
        <span>}</span>
      </div>
    </div>
  </div>

  <script>
    function setMode(mode) {
      const btnAll = document.getElementById('btn-all');
      const btnNeg3 = document.getElementById('btn-neg3');
      const btnPos3 = document.getElementById('btn-pos3');

      btnAll.className = 'btn';
      btnNeg3.className = 'btn';
      btnPos3.className = 'btn';

      const segLeft = document.querySelectorAll('.seg-left');
      const segMid = document.querySelectorAll('.seg-mid');
      const segRight = document.querySelectorAll('.seg-right');
      const holeNeg3 = document.querySelectorAll('.hole-neg3');
      const holePos3 = document.querySelectorAll('.hole-pos3');

      // Reset styles
      const allEls = document.querySelectorAll('.seg-left, .seg-mid, .seg-right, .hole-neg3, .hole-pos3');
      allEls.forEach(el => {
        el.classList.remove('dimmed', 'focused', 'focused-blue');
      });

      if (mode === 'all') {
        btnAll.classList.add('active');
      } else if (mode === 'neg3') {
        btnNeg3.classList.add('active-hole');
        segLeft.forEach(el => el.classList.add('dimmed'));
        segMid.forEach(el => el.classList.add('dimmed'));
        segRight.forEach(el => el.classList.add('dimmed'));
        holePos3.forEach(el => el.classList.add('dimmed'));
        holeNeg3.forEach(el => el.classList.add('focused'));
      } else if (mode === 'pos3') {
        btnPos3.classList.add('active-hole');
        segLeft.forEach(el => el.classList.add('dimmed'));
        segMid.forEach(el => el.classList.add('dimmed'));
        segRight.forEach(el => el.classList.add('dimmed'));
        holeNeg3.forEach(el => el.classList.add('dimmed'));
        holePos3.forEach(el => el.classList.add('focused'));
      }
    }
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background: #ffffff;
      color: #1e293b;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100vh;
      padding: 16px 12px;
      user-select: none;
    }

    .container {
      width: 100%;
      max-width: 500px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 16px;
      margin: auto 0;
    }

    /* Stepper Controls */
    .stepper {
      display: flex;
      gap: 6px;
      background: #f1f5f9;
      padding: 5px;
      border-radius: 24px;
      width: 100%;
      max-width: 440px;
      justify-content: space-between;
    }

    .step-btn {
      flex: 1;
      border: none;
      background: transparent;
      padding: 8px 10px;
      border-radius: 18px;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      cursor: pointer;
      text-align: center;
      transition: background-color 0.2s ease, color 0.2s ease, box-shadow 0.2s ease;
    }

    .step-btn.active {
      background: #ffffff;
      color: #0284c7;
      box-shadow: 0 1px 4px rgba(0,0,0,0.12);
    }

    /* Math Expression Area */
    .stage {
      width: 100%;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      gap: 16px;
      min-height: 170px;
    }

    .math-display {
      font-size: 24px;
      font-family: "Cambria Math", "STIX Two Math", "Times New Roman", serif;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      min-height: 76px;
      color: #0f172a;
      flex-wrap: wrap;
    }

    .var {
      font-style: italic;
      padding: 0 1px;
    }

    .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      padding: 0 4px;
    }

    .num {
      border-bottom: 2px solid #334155;
      padding-bottom: 3px;
      line-height: 1.1;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 3px;
    }

    .den {
      padding-top: 3px;
      line-height: 1.1;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 3px;
    }

    .sup {
      font-size: 0.65em;
      vertical-align: super;
      line-height: 0;
      position: relative;
      top: -0.45em;
    }

    /* Cancellation Strike Component */
    .cancelable {
      position: relative;
      display: inline-flex;
      align-items: center;
      padding: 0 2px;
    }

    .strike-line {
      position: absolute;
      top: 50%;
      left: -3px;
      right: -3px;
      height: 2.5px;
      background-color: #ef4444;
      border-radius: 2px;
      transform: rotate(-16deg);
      opacity: 0;
      transition: opacity 0.3s ease, transform 0.3s ease;
      pointer-events: none;
    }

    .strike-line.visible {
      opacity: 1;
    }

    .canceled-text {
      transition: color 0.3s ease;
    }

    .canceled-text.faded {
      color: #94a3b8;
    }

    .result-part {
      display: inline-flex;
      align-items: center;
      gap: 8px;
      animation: fadeIn 0.3s ease-in-out;
    }

    .highlight-res {
      background: #e0f2fe;
      color: #0369a1;
      padding: 2px 8px;
      border-radius: 6px;
      font-weight: bold;
    }

    /* Badges & Alerts */
    .badge-row {
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 8px;
      width: 100%;
    }

    .domain-badge {
      background: #f0fdf4;
      border: 1.5px solid #86efac;
      color: #15803d;
      padding: 8px 14px;
      border-radius: 8px;
      font-size: 13.5px;
      font-weight: 600;
      text-align: center;
      line-height: 1.4;
      width: 100%;
      max-width: 440px;
    }

    .warning-badge {
      background: #fef2f2;
      border: 1.5px solid #fca5a5;
      color: #b91c1c;
      padding: 7px 12px;
      border-radius: 8px;
      font-size: 13px;
      font-weight: 600;
      text-align: center;
      line-height: 1.4;
      width: 100%;
      max-width: 440px;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
    }

    /* Evaluation / Check Box */
    .test-box {
      width: 100%;
      max-width: 440px;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 10px;
      padding: 10px 14px;
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
      font-size: 13px;
    }

    .test-label {
      font-weight: 600;
      color: #475569;
      display: flex;
      align-items: center;
      gap: 4px;
    }

    .test-result {
      font-weight: 700;
      color: #dc2626;
      display: flex;
      align-items: center;
      gap: 6px;
      font-family: "Cambria Math", "STIX Two Math", "Times New Roman", serif;
      font-size: 15px;
    }

    .small-frac {
      font-size: 0.9em;
    }
    .small-frac .num { border-bottom-width: 1.5px; padding-bottom: 1px; }
    .small-frac .den { padding-top: 1px; }

    @keyframes fadeIn {
      from { opacity: 0; transform: translateY(4px); }
      to { opacity: 1; transform: translateY(0); }
    }

    @media (max-width: 420px) {
      .math-display { font-size: 20px; }
      .step-btn { padding: 6px 4px; font-size: 11.5px; }
      .domain-badge { font-size: 12px; padding: 6px 10px; }
      .warning-badge { font-size: 11.5px; padding: 6px 8px; }
      .test-box { flex-direction: column; align-items: flex-start; gap: 4px; }
    }
  </style>
</head>
<body>

  <div class="container">
    
    <div class="stepper" role="tablist">
      <button class="step-btn" id="btn0" onclick="setStep(0)">1. Original</button>
      <button class="step-btn" id="btn1" onclick="setStep(1)">2. Factor</button>
      <button class="step-btn active" id="btn2" onclick="setStep(2)">3. Cancel & Hole</button>
    </div>

    
    <div class="stage">
      <div class="math-display" id="mathDisplay"></div>
      <div class="badge-row" id="badgeRow"></div>
    </div>

    
    <div class="test-box">
      <div class="test-label">
        Plugging in <span style="font-family: 'Cambria Math', serif; font-style: italic;">x</span> = 2 into original:
      </div>
      <div class="test-result" id="testResult"></div>
    </div>
  </div>

  <script>
    const stepData = [
      {
        math: `
          <div class="frac">
            <span class="num"><span class="var">x</span><span class="sup">2</span> − 4</span>
            <span class="den"><span class="var">x</span> − 2</span>
          </div>
        `,
        badges: `
          <div class="warning-badge">⚠️ Restriction: Denominator cannot be zero (<span class="var">x</span> ≠ 2)</div>
        `,
        test: `
          <span class="frac small-frac">
            <span class="num">2<span class="sup">2</span> − 4</span>
            <span class="den">2 − 2</span>
          </span>
          = 
          <span class="frac small-frac">
            <span class="num">0</span>
            <span class="den">0</span>
          </span>
          <span style="font-family: system-ui; font-size: 12px; margin-left: 2px;">(undefined!)</span>
        `
      },
      {
        math: `
          <div class="frac">
            <span class="num">(<span class="var">x</span> − 2)(<span class="var">x</span> + 2)</span>
            <span class="den"><span class="var">x</span> − 2</span>
          </div>
        `,
        badges: `
          <div class="warning-badge">⚠️ Factor (<span class="var">x</span> − 2) in numerator & denominator reveals the hole</div>
        `,
        test: `
          <span class="frac small-frac">
            <span class="num">(0)(4)</span>
            <span class="den">0</span>
          </span>
          = 
          <span class="frac small-frac">
            <span class="num">0</span>
            <span class="den">0</span>
          </span>
          <span style="font-family: system-ui; font-size: 12px; margin-left: 2px;">(undefined!)</span>
        `
      },
      {
        math: `
          <div class="frac">
            <span class="num">
              <span class="cancelable">
                <span class="canceled-text faded">(<span class="var">x</span> − 2)</span>
                <span class="strike-line visible"></span>
              </span>(<span class="var">x</span> + 2)
            </span>
            <span class="den">
              <span class="cancelable">
                <span class="canceled-text faded"><span class="var">x</span> − 2</span>
                <span class="strike-line visible"></span>
              </span>
            </span>
          </div>
          <div class="result-part">
            <span>=</span>
            <span class="highlight-res"><span class="var">x</span> + 2</span>
          </div>
        `,
        badges: `
          <div class="domain-badge">
            Domain: {<span class="var">x</span> ∈ ℝ | <span class="var">x</span> ≠ 2} &nbsp;or&nbsp; (−∞, 2) ∪ (2, ∞)
          </div>
          <div class="warning-badge">
            ⚠️ Hidden Hole at <span class="var">x</span> = 2 (still undefined in original!)
          </div>
        `,
        test: `
          <span style="font-family: system-ui; font-size: 12.5px; color: #475569; font-weight: normal; margin-right: 2px;">Original gives</span>
          <span class="frac small-frac">
            <span class="num">0</span>
            <span class="den">0</span>
          </span>
          <span style="font-family: system-ui; font-size: 12.5px;">(undefined!)</span>
        `
      }
    ];

    function setStep(idx) {
      for (let i = 0; i < 3; i++) {
        document.getElementById('btn' + i).classList.toggle('active', i === idx);
      }

      const stage = stepData[idx];
      document.getElementById('mathDisplay').innerHTML = stage.math;
      document.getElementById('badgeRow').innerHTML = stage.badges;
      document.getElementById('testResult').innerHTML = stage.test;
    }

    // Initialize with Step 3 (Cancel & Hole) as default
    setStep(2);
  </script>
</body>
</html>

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <meta name="aspect-ratio" content="4:3">
  <style>
    * {
      box-sizing: border-box;
      margin: 0;
      padding: 0;
    }

    body {
      font-family: system-ui, -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, sans-serif;
      background-color: #f8f9fa;
      color: #1e2945;
      padding: 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }

    .diagram {
      width: 100%;
      max-width: 520px;
      display: flex;
      flex-direction: column;
      gap: 14px;
      align-items: center;
    }

    /* Main Anatomy Layout */
    .anatomy-container {
      display: grid;
      grid-template-columns: auto 1fr;
      align-items: center;
      gap: 16px 20px;
      width: 100%;
      padding: 6px 0;
    }

    .fraction-wrap {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      font-size: 26px;
      font-weight: 700;
      padding: 4px 8px;
    }

    .num-box {
      color: #2a9d8f;
      background: #e8f6f5;
      border: 2px solid #2a9d8f;
      border-radius: 8px;
      padding: 4px 14px;
      transition: background 0.2s ease;
    }

    .frac-bar {
      width: 100%;
      height: 3px;
      background-color: #1e2945;
      border-radius: 2px;
      margin: 6px 0;
    }

    .den-box {
      color: #e63946;
      background: #fde8ea;
      border: 2px solid #e63946;
      border-radius: 8px;
      padding: 4px 14px;
      transition: background 0.2s ease;
    }

    .callout {
      display: flex;
      align-items: center;
      gap: 8px;
      font-size: 13.5px;
      font-weight: 600;
      line-height: 1.3;
    }

    .callout-num {
      color: #1b685f;
      background: #ffffff;
      border: 1px solid #bce3df;
      padding: 6px 12px;
      border-radius: 6px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.04);
    }

    .callout-den {
      color: #b01927;
      background: #ffffff;
      border: 1px solid #f8bdc2;
      padding: 6px 12px;
      border-radius: 6px;
      box-shadow: 0 1px 3px rgba(0,0,0,0.04);
    }

    /* Equation Section */
    .restriction-panel {
      width: 100%;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-left: 4px solid #e63946;
      border-radius: 8px;
      padding: 10px 14px;
      display: flex;
      flex-wrap: wrap;
      align-items: center;
      justify-content: space-between;
      gap: 8px;
    }

    .math-steps {
      display: flex;
      align-items: center;
      gap: 8px;
      font-size: 15px;
      font-weight: 600;
      color: #1e2945;
    }

    .step-badge {
      background: #f1f5f9;
      padding: 3px 8px;
      border-radius: 5px;
    }

    .arrow {
      color: #94a3b8;
      font-weight: bold;
    }

    .excluded-badge {
      background: #fde8ea;
      color: #e63946;
      padding: 3px 8px;
      border-radius: 5px;
      border: 1px solid #f8bdc2;
    }

    /* Interactive Tester */
    .tester {
      width: 100%;
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 10px 14px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .tester-header {
      display: flex;
      align-items: center;
      justify-content: space-between;
      font-size: 12px;
      font-weight: 700;
      color: #64748b;
      text-transform: uppercase;
      letter-spacing: 0.5px;
    }

    .btn-row {
      display: flex;
      gap: 8px;
    }

    .test-btn {
      flex: 1;
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      color: #1e2945;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 4px;
      border-radius: 6px;
      cursor: pointer;
      transition: background 0.15s ease, border-color 0.15s ease;
      text-align: center;
    }

    .test-btn.active {
      background: #1e2945;
      color: #ffffff;
      border-color: #1e2945;
    }

    .test-btn.danger-btn.active {
      background: #e63946;
      color: #ffffff;
      border-color: #e63946;
    }

    .eval-display {
      font-size: 14px;
      font-weight: 600;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      padding: 6px;
      background: #f8fafc;
      border-radius: 6px;
      min-height: 36px;
    }

    .status-ok {
      color: #2a9d8f;
    }

    .status-err {
      color: #e63946;
      font-weight: 700;
    }

    @media (max-width: 420px) {
      .anatomy-container {
        gap: 12px 10px;
      }
      .fraction-wrap {
        font-size: 22px;
      }
      .callout {
        font-size: 12px;
      }
      .math-steps {
        font-size: 13px;
        flex-wrap: wrap;
      }
    }
  </style>
</head>
<body>

  <div class="diagram">

    
    <div class="anatomy-container">
      <div class="fraction-wrap">
        <div class="num-box" id="dispNum">2x + 1</div>
        <div class="frac-bar"></div>
        <div class="den-box" id="dispDen">x − 5</div>
      </div>

      <div style="display: flex; flex-direction: column; gap: 14px;">
        <div class="callout callout-num">
          <span>← Numerator<br><span style="font-size:11.5px; opacity:0.85; font-weight:500;">Can be any real number</span></span>
        </div>
        <div class="callout callout-den">
          <span>← Denominator<br><span style="font-size:11.5px; opacity:0.9; font-weight:700;">Cannot equal 0!</span></span>
        </div>
      </div>
    </div>

    
    <div class="restriction-panel">
      <div class="math-steps">
        <span class="step-badge">x − 5 = 0</span>
        <span class="arrow">→</span>
        <span class="step-badge">x = 5</span>
      </div>
      <div class="excluded-badge">Excluded Value: x ≠ 5</div>
    </div>

    
    <div class="tester">
      <div class="tester-header">
        <span>Test Values</span>
        <span>Interactive Check</span>
      </div>
      <div class="btn-row">
        <button class="test-btn active" onclick="testVal(3, this)">x = 3</button>
        <button class="test-btn danger-btn" onclick="testVal(5, this)">x = 5 ⚠️</button>
        <button class="test-btn" onclick="testVal(7, this)">x = 7</button>
      </div>
      <div class="eval-display" id="resultBox">
        <span><span style="color:#2a9d8f">7</span> / <span style="color:#e63946">−2</span> = <b>−3.5</b></span>
        <span class="status-ok">✓ Valid</span>
      </div>
    </div>

  </div>

  <script>
    function testVal(val, btn) {
      document.querySelectorAll('.test-btn').forEach(b => b.classList.remove('active'));
      btn.classList.add('active');

      const num = 2 * val + 1;
      const den = val - 5;
      const resBox = document.getElementById('resultBox');
      const dispNum = document.getElementById('dispNum');
      const dispDen = document.getElementById('dispDen');

      dispNum.textContent = `2(${val}) + 1`;
      dispDen.textContent = `${val} − 5`;

      if (den === 0) {
        resBox.innerHTML = `<span><span style="color:#2a9d8f">${num}</span> / <span style="color:#e63946">0</span></span> <span class="status-err">💥 Undefined (Division by 0)</span>`;
      } else {
        const result = (num / den).toLocaleString(undefined, { maximumFractionDigits: 2 });
        resBox.innerHTML = `<span><span style="color:#2a9d8f">${num}</span> / <span style="color:#e63946">${den}</span> = <b>${result}</b></span> <span class="status-ok">✓ Valid</span>`;
      }
    }
  </script>

</body>
</html>

OGM.10.ALG.5

Aligned learning resources

Related diagrams