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  <title>Simplifying Rational Expressions</title>
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</head>
<body>

  <div class="container">
    
    <nav class="stepper-nav" aria-label="Step Navigation">
      <button class="step-btn active" onclick="setStep(0)" id="tab-0">
        <span class="num">Step 1</span>
        <span class="label">Extract GCF</span>
      </button>
      <button class="step-btn" onclick="setStep(1)" id="tab-1">
        <span class="num">Step 2</span>
        <span class="label">Diff of Squares</span>
      </button>
      <button class="step-btn" onclick="setStep(2)" id="tab-2">
        <span class="num">Step 3</span>
        <span class="label">Cancel Factors</span>
      </button>
    </nav>

    
    <div class="stage">
      
      <div class="step-view active" id="view-0">
        <div class="badge">Factor out greatest common factors</div>
        <div class="math-row">
          <div class="frac">
            <div class="num-line">6x² − 24</div>
            <div class="den-line">3x + 6</div>
          </div>
          <span>=</span>
          <div class="frac">
            <div class="num-line"><span class="hl-gcf">6</span>(x² − 4)</div>
            <div class="den-line"><span class="hl-gcf">3</span>(x + 2)</div>
          </div>
        </div>
      </div>

      
      <div class="step-view" id="view-1">
        <div class="badge">x² − 4 = (x − 2)(x + 2)</div>
        <div class="math-row">
          <div class="frac">
            <div class="num-line">6(x² − 4)</div>
            <div class="den-line">3(x + 2)</div>
          </div>
          <span>=</span>
          <div class="frac">
            <div class="num-line">6<span class="hl-diff">(x − 2)(x + 2)</span></div>
            <div class="den-line">3(x + 2)</div>
          </div>
        </div>
      </div>

      
      <div class="step-view" id="view-2">
        <div class="badge">Cancel common factors</div>
        <div class="math-row">
          <div class="frac">
            <div class="num-line">
              <span class="strike-box struck">
                6
                <span class="replace-tag top show">2</span>
              </span>
              <span>(x − 2)</span>
              <span class="strike-box struck">
                (x + 2)
              </span>
            </div>
            <div class="den-line">
              <span class="strike-box struck">
                3
                <span class="replace-tag bot show">1</span>
              </span>
              <span class="strike-box struck">
                (x + 2)
              </span>
            </div>
          </div>
          <span>=</span>
          <div class="result-box">
            2(x − 2)
          </div>
        </div>
      </div>
    </div>

    
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      <button class="ctrl-btn" onclick="prevStep()" aria-label="Previous step">← Prev</button>
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</html>

Simplifying Algebraic Fractions Using Factorisation

<!DOCTYPE html>
<html lang="en">
<head>
  <meta charset="UTF-8">
  <meta name="viewport" content="width=device-width, initial-scale=1.0">
  <title>Simplifying Rational Expressions & Domain Restrictions</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
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      font-family: system-ui, -apple-system, "Segoe UI", Roboto, sans-serif;
      background: #f8fafc;
      color: #0f172a;
      min-height: 100vh;
      display: flex;
      flex-direction: column;
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      justify-content: center;
      padding: 16px 12px;
      user-select: none;
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      width: 100%;
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      display: flex;
      flex-direction: column;
      gap: 14px;
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      font-size: 12px;
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      min-width: 38px;
      transition: background 0.2s;
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      background: #f1f5f9;
    }

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      position: relative;
      width: 100%;
      min-height: 270px;
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      border-radius: 12px;
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      margin-bottom: 4px;
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      top: 50%;
      height: 3px;
      background: #ef4444;
      transform: rotate(-14deg);
      border-radius: 2px;
    }

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      display: inline-flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
      padding: 6px 14px;
      border-radius: 20px;
      font-size: 13px;
      font-weight: 600;
      text-align: center;
      max-width: 95%;
    }
    .badge-blue {
      background: #eff6ff;
      color: #1d4ed8;
      border: 1px solid #bfdbfe;
    }
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      background: #fffbeb;
      color: #b45309;
      border: 1.5px solid #f59e0b;
      box-shadow: 0 2px 6px rgba(245, 158, 11, 0.15);
      font-size: 13px;
      line-height: 1.35;
    }
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      background: #f0fdf4;
      color: #15803d;
      border: 1px solid #86efac;
    }

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      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 4px;
      margin-top: 10px;
      font-size: 12px;
      color: #475569;
      text-align: center;
    }
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      font-size: 11px;
      color: #64748b;
    }
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      background: #fff7ed;
      border-left: 3px solid #f97316;
      padding: 6px 10px;
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      font-size: 11.5px;
      color: #9a3412;
      margin-top: 8px;
      max-width: 480px;
      text-align: left;
    }

    /* Responsive adjustments */
    @media (max-width: 440px) {
      .math-expr {
        font-size: 20px;
      }
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        font-size: 11px;
        padding: 6px 2px;
      }
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        font-size: 12px;
        padding: 5px 10px;
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        min-height: 290px;
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  </style>
</head>
<body>

<div class="diagram-root">
  <div class="title-area">
    <h1>Simplifying Rational Expressions</h1>
    <p>Always track domain restrictions before canceling common factors</p>
  </div>

  
  <div class="controls">
    <div class="step-tabs">
      <button class="step-tab active" data-step="0">1. Original</button>
      <button class="step-tab" data-step="1">2. Factor</button>
      <button class="step-tab" data-step="2">3. Restrict</button>
      <button class="step-tab" data-step="3">4. Cancel</button>
    </div>
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      <span id="playIcon">⏸</span>
    </button>
  </div>

  
  <div class="stage">
    
    <div class="step-panel active" id="step-0">
      <div class="math-expr">
        <span class="frac">
          <span class="num">2<i>x</i><sup>2</sup> &minus; 5<i>x</i> &minus; 3</span>
          <span class="den"><i>x</i><sup>2</sup> &minus; 9</span>
        </span>
      </div>
      <span class="badge badge-blue">Original Expression</span>
      <div class="step-details">
        <span>Quadratic numerator and difference of squares denominator</span>
      </div>
    </div>

    
    <div class="step-panel" id="step-1">
      <div class="math-expr">
        <span class="frac">
          <span class="num">(2<i>x</i> + 1)(<i>x</i> &minus; 3)</span>
          <span class="den">(<i>x</i> + 3)(<i>x</i> &minus; 3)</span>
        </span>
      </div>
      <span class="badge badge-blue">Step 1: Factored Form</span>
      <div class="step-details">
        <span>Numerator: (2<i>x</i> + 1)(<i>x</i> &minus; 3) &nbsp;|&nbsp; Denominator: (<i>x</i> + 3)(<i>x</i> &minus; 3)</span>
        <span class="subnote">Both polynomials factored completely into linear binomials</span>
      </div>
    </div>

    
    <div class="step-panel" id="step-2">
      <div class="math-expr">
        <span class="frac">
          <span class="num">(2<i>x</i> + 1)(<i>x</i> &minus; 3)</span>
          <span class="den hl-den-restr">(<i>x</i> + 3)(<i>x</i> &minus; 3)</span>
        </span>
      </div>
      <span class="badge badge-amber">⚠️ Denominator &ne; 0 &nbsp;&rArr;&nbsp; <i>x</i> &ne; 3, &minus;3</span>
      <div class="warning-callout">
        <strong>CRITICAL RULE:</strong> Find restrictions <em>BEFORE</em> canceling! Even if a factor disappears during simplification, values making the original denominator 0 remain excluded from the domain.
      </div>
    </div>

    
    <div class="step-panel" id="step-3">
      <div class="math-expr">
        <span class="frac">
          <span class="num">(2<i>x</i> + 1)<span class="cancel-term">(<i>x</i> &minus; 3)</span></span>
          <span class="den">(<i>x</i> + 3)<span class="cancel-term">(<i>x</i> &minus; 3)</span></span>
        </span>
        <span style="margin: 0 10px; font-family: sans-serif; font-size: 20px; color: #64748b;">=</span>
        <span class="frac">
          <span class="num hl-term">2<i>x</i> + 1</span>
          <span class="den hl-term"><i>x</i> + 3</span>
        </span>
      </div>
      <span class="badge badge-green">✓ Simplified Form with Domain Restriction</span>
      <div class="step-details">
        <span style="font-weight: 600; color: #15803d;">Final Answer: <sup>(2<i>x</i> + 1)</sup>/<sub>(<i>x</i> + 3)</sub> , where <i>x</i> &ne; 3, &minus;3</span>
        <span class="subnote">Common factor (<i>x</i> &minus; 3) canceled; restriction <i>x</i> &ne; 3 creates a removable discontinuity (hole).</span>
      </div>
    </div>
  </div>
</div>

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    if (isPlaying) {
      pauseAutoPlay();
    } else {
      startAutoPlay();
    }
  });

  // Start autoplay on load
  startAutoPlay();
</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: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, "Helvetica Neue", Arial, sans-serif;
      color: #1e2945;
      background: transparent;
      padding: 16px 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 380px;
      max-width: 640px;
      margin: 0 auto;
    }

    /* Top Rule Badge */
    .badge-container {
      display: flex;
      align-items: center;
      justify-content: center;
      margin-bottom: 8px;
    }

    .badge {
      display: inline-flex;
      align-items: center;
      gap: 10px;
      padding: 8px 18px;
      background: #f5f3ff;
      border: 1.5px solid #8b5cf6;
      border-radius: 999px;
      font-size: 15px;
      font-weight: 700;
      color: #6d28d9;
      box-shadow: 0 2px 8px rgba(139, 92, 246, 0.12);
    }

    .badge-label {
      font-size: 12px;
      letter-spacing: 0.5px;
      text-transform: uppercase;
      color: #7c3aed;
      background: #ede9fe;
      padding: 2px 8px;
      border-radius: 6px;
      font-weight: 800;
    }

    /* Math typography & layout */
    .math {
      font-family: "Cambria Math", "Times New Roman", Times, serif;
      font-style: italic;
      display: inline-flex;
      align-items: center;
      font-size: 1.15em;
    }

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

    .math span.op {
      font-style: normal;
      margin: 0 4px;
    }

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

    .frac > .num {
      border-bottom: 1.8px solid currentColor;
      padding: 0 4px 2px 4px;
      width: 100%;
      display: block;
    }

    .frac > .den {
      padding: 2px 4px 0 4px;
      width: 100%;
      display: block;
    }

    .hl-blue {
      color: #0284c7;
      font-weight: bold;
      background: rgba(34, 183, 255, 0.12);
      padding: 1px 4px;
      border-radius: 4px;
    }

    .hl-purple {
      color: #7c3aed;
      font-weight: bold;
      background: rgba(139, 92, 246, 0.12);
      padding: 1px 4px;
      border-radius: 4px;
    }

    .hl-neg {
      color: #e11d48;
      font-weight: 800;
      font-style: normal;
    }

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

    .strike-wrap::after {
      content: '';
      position: absolute;
      left: -2px;
      right: -2px;
      top: 50%;
      height: 2px;
      background: #ef4444;
      transform: rotate(-16deg);
      border-radius: 2px;
    }

    /* Animated Stage */
    .stage {
      position: relative;
      width: 100%;
      min-height: 200px;
      display: flex;
      align-items: center;
      justify-content: center;
      margin: 12px 0;
    }

    .step-panel {
      position: absolute;
      inset: 0;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      opacity: 0;
      pointer-events: none;
      transform: translateY(8px);
      transition: opacity 0.3s ease, transform 0.3s ease;
      text-align: center;
      padding: 8px 12px;
    }

    .step-panel.active {
      opacity: 1;
      pointer-events: auto;
      transform: translateY(0);
    }

    .step-tag {
      font-size: 12px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
      margin-bottom: 12px;
    }

    .math-display {
      font-size: 25px;
      line-height: 1.5;
      display: flex;
      align-items: center;
      justify-content: center;
      flex-wrap: wrap;
      gap: 8px;
    }

    .step-note {
      margin-top: 14px;
      font-size: 14px;
      color: #475569;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 6px 14px;
      max-width: 90%;
      line-height: 1.4;
    }

    /* Controls */
    .controls {
      display: flex;
      align-items: center;
      gap: 8px;
      flex-wrap: wrap;
      justify-content: center;
      width: 100%;
      margin-top: 6px;
    }

    .step-btn {
      appearance: none;
      border: 1.5px solid #cbd5e1;
      background: #ffffff;
      color: #475569;
      font-size: 13px;
      font-weight: 600;
      padding: 8px 14px;
      border-radius: 8px;
      cursor: pointer;
      transition: background-color 0.2s ease, border-color 0.2s ease, color 0.2s ease, box-shadow 0.2s ease;
    }

    .step-btn:hover {
      border-color: #0284c7;
      color: #0284c7;
    }

    .step-btn.active {
      background: #0284c7;
      border-color: #0284c7;
      color: #ffffff;
      box-shadow: 0 2px 8px rgba(2, 132, 199, 0.3);
    }

    .play-btn {
      appearance: none;
      border: 1.5px solid #8b5cf6;
      background: #8b5cf6;
      color: #ffffff;
      width: 36px;
      height: 36px;
      border-radius: 8px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 14px;
      cursor: pointer;
      transition: background-color 0.2s ease, opacity 0.2s ease;
    }

    .play-btn:hover {
      opacity: 0.9;
    }

    @media (max-width: 480px) {
      .math-display { font-size: 19px; }
      .badge { font-size: 13px; padding: 6px 12px; gap: 6px; }
      .step-btn { font-size: 12px; padding: 6px 10px; }
      .step-note { font-size: 12px; }
    }
  </style>
</head>
<body>

  
  <div class="badge-container">
    <div class="badge">
      <span class="badge-label">Rule</span>
      <span class="math">
        <span class="frac">
          <span class="num"><var>a</var> − <var>b</var></span>
          <span class="den"><var>b</var> − <var>a</var></span>
        </span>
        <span class="op">=</span> −1
      </span>
    </div>
  </div>

  
  <div class="stage">
    
    <div class="step-panel active" id="step0">
      <div class="step-tag">Step 1: Spot Opposite Factors</div>
      <div class="math-display">
        <span class="math">
          <span class="frac">
            <span class="num"><var>x</var><span class="hl-blue">(<var>x</var> − 4)</span></span>
            <span class="den"><span class="hl-purple">(4 − <var>x</var>)</span>(4 + <var>x</var>)</span>
          </span>
        </span>
      </div>
      <div class="step-note">
        Notice that <span class="hl-blue">(x − 4)</span> and <span class="hl-purple">(4 − x)</span> are exact opposites.
      </div>
    </div>

    
    <div class="step-panel" id="step1">
      <div class="step-tag">Step 2: Factor Out −1</div>
      <div class="math-display">
        <span class="math">
          <span class="frac">
            <span class="num"><var>x</var><span class="hl-blue">(<var>x</var> − 4)</span></span>
            <span class="den"><span class="hl-neg">(−1)</span><span class="hl-purple">(<var>x</var> − 4)</span>(<var>x</var> + 4)</span>
          </span>
        </span>
      </div>
      <div class="step-note">
        Rewrite <span class="hl-purple">(4 − x)</span> as <span class="hl-neg">−1</span><span class="hl-purple">(x − 4)</span> to match the numerator.
      </div>
    </div>

    
    <div class="step-panel" id="step2">
      <div class="step-tag">Step 3: Cancel Common Factors</div>
      <div class="math-display">
        <span class="math">
          <span class="frac">
            <span class="num"><var>x</var><span class="strike-wrap hl-blue">(<var>x</var> − 4)</span></span>
            <span class="den"><span class="hl-neg">−1</span><span class="strike-wrap hl-purple">(<var>x</var> − 4)</span>(<var>x</var> + 4)</span>
          </span>
          <span class="op">=</span>
          <span class="frac">
            <span class="num"><var>x</var></span>
            <span class="den">−1(<var>x</var> + 4)</span>
          </span>
          <span class="op">=</span>
          −<span class="frac">
            <span class="num"><var>x</var></span>
            <span class="den"><var>x</var> + 4</span>
          </span>
        </span>
      </div>
      <div class="step-note">
        Divide out the shared <span class="strike-wrap">(x − 4)</span> factor.
      </div>
    </div>
  </div>

  
  <div class="controls">
    <button class="step-btn active" data-step="0">1. Spot Opposites</button>
    <button class="step-btn" data-step="1">2. Factor Out −1</button>
    <button class="step-btn" data-step="2">3. Cancel</button>
    <button class="play-btn" id="playBtn" title="Auto play / Pause" aria-label="Auto play / Pause">⏸</button>
  </div>

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

    const panels = [
      document.getElementById('step0'),
      document.getElementById('step1'),
      document.getElementById('step2')
    ];
    const buttons = document.querySelectorAll('.step-btn');
    const playBtn = document.getElementById('playBtn');

    function setStep(idx) {
      currentStep = idx;
      panels.forEach((p, i) => p.classList.toggle('active', i === idx));
      buttons.forEach((b, i) => b.classList.toggle('active', i === idx));
    }

    function nextStep() {
      setStep((currentStep + 1) % 3);
    }

    function startAuto() {
      if (timer) clearInterval(timer);
      timer = setInterval(nextStep, 3500);
      isPlaying = true;
      playBtn.textContent = '⏸';
    }

    function stopAuto() {
      if (timer) clearInterval(timer);
      isPlaying = false;
      playBtn.textContent = '▶';
    }

    buttons.forEach(btn => {
      btn.addEventListener('click', () => {
        stopAuto();
        setStep(parseInt(btn.dataset.step, 10));
      });
    });

    playBtn.addEventListener('click', () => {
      if (isPlaying) {
        stopAuto();
      } else {
        startAuto();
      }
    });

    startAuto();
  </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 Algebraic Fractions</title>
  <style>
    * { box-sizing: border-box; margin: 0; padding: 0; }
    body {
      font-family: system-ui, -apple-system, sans-serif;
      background: #f8f9fa;
      color: #1e2945;
      padding: 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: space-between;
      min-height: 100%;
    }

    .main-wrap {
      width: 100%;
      max-width: 580px;
      display: flex;
      flex-direction: column;
      gap: 14px;
    }

    /* Step Navigation */
    .steps-nav {
      display: flex;
      gap: 6px;
      background: #e2e8f0;
      padding: 4px;
      border-radius: 8px;
    }

    .step-btn {
      flex: 1;
      border: none;
      background: transparent;
      padding: 6px 4px;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      border-radius: 6px;
      cursor: pointer;
      transition: all 0.2s ease;
      text-align: center;
      white-space: nowrap;
    }

    .step-btn.active {
      background: #ffffff;
      color: #1e2945;
      box-shadow: 0 1px 3px rgba(0,0,0,0.1);
    }

    /* Transformation Stage */
    .stage-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 120px;
      position: relative;
    }

    .math-display {
      font-size: 24px;
      font-weight: 600;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      letter-spacing: 0.5px;
    }

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

    .num {
      border-bottom: 2px solid #1e2945;
      padding-bottom: 3px;
    }

    .den {
      padding-top: 3px;
    }

    .badge-hl {
      display: inline-block;
      padding: 1px 4px;
      border-radius: 4px;
      transition: all 0.3s ease;
    }

    .hl-blue {
      background: #e0f2fe;
      color: #0284c7;
    }

    .hl-green {
      background: #dcfce7;
      color: #15803d;
    }

    .strike {
      position: relative;
      color: #94a3b8;
    }

    .strike::after {
      content: '';
      position: absolute;
      left: -2px;
      right: -2px;
      top: 50%;
      height: 2px;
      background: #ef4444;
      transform: rotate(-12deg);
    }

    .step-desc {
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      margin-top: 10px;
    }

    /* Evaluator Section */
    .eval-card {
      background: #ffffff;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 14px 16px;
      display: flex;
      flex-direction: column;
      gap: 12px;
    }

    .controls-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
      gap: 12px;
      flex-wrap: wrap;
    }

    .slider-wrap {
      display: flex;
      align-items: center;
      gap: 10px;
      flex: 1;
      min-width: 200px;
    }

    input[type=range] {
      flex: 1;
      accent-color: #22b7ff;
      height: 6px;
      cursor: pointer;
    }

    .chips {
      display: flex;
      gap: 6px;
    }

    .chip {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #334155;
      padding: 3px 8px;
      border-radius: 6px;
      font-size: 12px;
      font-weight: 600;
      cursor: pointer;
    }

    .chip.active {
      background: #22b7ff;
      border-color: #22b7ff;
      color: #ffffff;
    }

    /* Comparison Grid */
    .compare-grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 10px;
    }

    .calc-box {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 10px;
      text-align: center;
    }

    .calc-box.highlight {
      border-color: #86efac;
      background: #f0fdf4;
    }

    .calc-title {
      font-size: 11px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
      margin-bottom: 6px;
    }

    .calc-expr {
      font-size: 14px;
      font-weight: 600;
      color: #1e2945;
      margin-bottom: 4px;
      min-height: 28px;
      display: flex;
      align-items: center;
      justify-content: center;
    }

    .calc-res {
      font-size: 18px;
      font-weight: 700;
      color: #0284c7;
    }

    .calc-box.highlight .calc-res {
      color: #15803d;
    }

    .equals-pill {
      grid-column: span 2;
      text-align: center;
      font-size: 12px;
      font-weight: 600;
      color: #15803d;
      background: #dcfce7;
      padding: 4px 8px;
      border-radius: 6px;
    }
  </style>
</head>
<body>

  <div class="main-wrap">
    
    <div class="steps-nav">
      <button class="step-btn active" onclick="setStep(0)">1. Factor</button>
      <button class="step-btn" onclick="setStep(1)">2. Cancel</button>
      <button class="step-btn" onclick="setStep(2)">3. Result</button>
    </div>

    
    <div class="stage-card">
      <div id="mathStage" class="math-display"></div>
      <div id="stepDesc" class="step-desc"></div>
    </div>

    
    <div class="eval-card">
      <div class="controls-row">
        <div class="slider-wrap">
          <span style="font-size:14px; font-weight:700;">x = <span id="xValLabel" style="color:#0284c7;">100</span></span>
          <input type="range" id="xSlider" min="4" max="100" value="100" step="1" oninput="updateX(this.value)">
        </div>
        <div class="chips">
          <button class="chip" onclick="setX(5)">x=5</button>
          <button class="chip" onclick="setX(10)">x=10</button>
          <button class="chip active" id="chip100" onclick="setX(100)">x=100</button>
        </div>
      </div>

      <div class="compare-grid">
        <div class="calc-box">
          <div class="calc-title">Original Expression</div>
          <div class="calc-expr" id="origExpr"></div>
          <div class="calc-res" id="origRes"></div>
        </div>
        <div class="calc-box highlight">
          <div class="calc-title">Simplified Form</div>
          <div class="calc-expr" id="simpExpr"></div>
          <div class="calc-res" id="simpRes"></div>
        </div>
        <div class="equals-pill">
          Both equal <span id="commonRes">103</span> for all valid x (x ≠ 3)
        </div>
      </div>
    </div>
  </div>

  <script>
    let currentStep = 0;
    let currentX = 100;

    const stepsData = [
      {
        html: `<div class="frac"><span class="num badge-hl hl-blue">(x - 3)(x + 3)</span><span class="den">x - 3</span></div>`,
        desc: "Factor Numerator (Difference of Squares)"
      },
      {
        html: `<div class="frac"><span class="num"><span class="strike">(x - 3)</span><span class="badge-hl hl-green">(x + 3)</span></span><span class="den"><span class="strike">x - 3</span></span></div>`,
        desc: "Cancel Common Factor (x - 3)"
      },
      {
        html: `<span>=</span> <span class="badge-hl hl-green" style="font-size:28px;">x + 3</span>`,
        desc: "Simplified Form"
      }
    ];

    function setStep(idx) {
      currentStep = idx;
      document.querySelectorAll('.step-btn').forEach((btn, i) => {
        btn.classList.toggle('active', i === idx);
      });
      document.getElementById('mathStage').innerHTML = stepsData[idx].html;
      document.getElementById('stepDesc').textContent = stepsData[idx].desc;
    }

    function setX(val) {
      document.getElementById('xSlider').value = val;
      updateX(val);
    }

    function updateX(val) {
      currentX = parseInt(val, 10);
      document.getElementById('xValLabel').textContent = currentX;

      document.querySelectorAll('.chip').forEach(c => {
        c.classList.toggle('active', c.textContent === `x=${currentX}`);
      });

      const num = (currentX * currentX) - 9;
      const den = currentX - 3;
      const ans = currentX + 3;

      document.getElementById('origExpr').innerHTML = `<div class="frac" style="font-size:13px;"><span class="num">${num}</span><span class="den">${den}</span></div>`;
      document.getElementById('origRes').textContent = `= ${ans}`;

      document.getElementById('simpExpr').innerHTML = `${currentX} + 3`;
      document.getElementById('simpRes').textContent = `= ${ans}`;

      document.getElementById('commonRes').textContent = ans;
    }

    // Initialize
    setStep(0);
    updateX(100);
  </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;
      color: #1e2945;
      background: transparent;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
    }
    .title {
      font-size: 18px;
      font-weight: 700;
      margin-bottom: 12px;
      letter-spacing: -0.01em;
      text-align: center;
    }
    .grid {
      display: grid;
      grid-template-columns: 1fr 1fr;
      gap: 12px;
      width: 100%;
      max-width: 620px;
    }
    @media (max-width: 480px) {
      .grid {
        grid-template-columns: 1fr;
        gap: 10px;
      }
    }
    .panel {
      border-radius: 12px;
      padding: 14px 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      text-align: center;
      position: relative;
    }
    .panel-do {
      background: #f0fdf4;
      border: 1.5px solid #86efac;
    }
    .panel-dont {
      background: #fef2f2;
      border: 1.5px solid #fca5a5;
    }
    .badge {
      display: inline-flex;
      align-items: center;
      gap: 4px;
      font-size: 13px;
      font-weight: 700;
      padding: 4px 10px;
      border-radius: 20px;
      text-transform: uppercase;
      letter-spacing: 0.04em;
      margin-bottom: 12px;
    }
    .badge-do {
      background: #dcfce7;
      color: #15803d;
    }
    .badge-dont {
      background: #fee2e2;
      color: #b91c1c;
    }
    .math-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 8px;
      font-family: 'Cambria Math', 'KaTeX_Main', 'Times New Roman', serif;
      font-size: 20px;
      min-height: 72px;
    }
    .frac {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      vertical-align: middle;
      padding: 0 4px;
    }
    .num {
      padding-bottom: 3px;
      border-bottom: 2px solid #1e2945;
      display: flex;
      align-items: center;
      justify-content: center;
    }
    .den {
      padding-top: 3px;
      display: flex;
      align-items: center;
      justify-content: center;
    }
    .factor-cancel {
      position: relative;
      color: #15803d;
      font-weight: bold;
      padding: 0 2px;
    }
    .factor-cancel::after {
      content: '';
      position: absolute;
      left: -2px;
      right: -2px;
      top: 50%;
      height: 2px;
      background: #15803d;
      transform: rotate(-35deg);
      border-radius: 1px;
    }
    .term-error {
      position: relative;
      color: #b91c1c;
      font-weight: bold;
      padding: 0 2px;
    }
    .term-error::after {
      content: '✕';
      position: absolute;
      left: 50%;
      top: 50%;
      transform: translate(-50%, -50%);
      color: #dc2626;
      font-size: 22px;
      font-weight: 900;
      font-family: system-ui, sans-serif;
      pointer-events: none;
    }
    .subtag {
      margin-top: 10px;
      font-size: 13px;
      font-weight: 600;
      padding: 3px 8px;
      border-radius: 6px;
    }
    .subtag-do {
      color: #166534;
      background: rgba(22, 101, 52, 0.08);
    }
    .subtag-dont {
      color: #991b1b;
      background: rgba(153, 27, 27, 0.08);
    }
    .toggle-btn {
      margin-top: 12px;
      background: #ffffff;
      border: 1.5px solid #cbd5e1;
      color: #1e2945;
      font-size: 13px;
      font-weight: 600;
      padding: 6px 14px;
      border-radius: 8px;
      cursor: pointer;
      box-shadow: 0 1px 2px rgba(0,0,0,0.05);
      transition: background 0.2s, border-color 0.2s;
    }
    .toggle-btn:active {
      background: #f1f5f9;
    }
  </style>
</head>
<body>

  <div class="title">Factors vs. Terms</div>

  <div class="grid">
    
    <div class="panel panel-do">
      <div class="badge badge-do">✓ Cancel Factors</div>
      
      <div class="math-row" id="mathDo">
        <div class="frac">
          <div class="num"><span class="factor-cancel">x</span>(x + 4)</div>
          <div class="den"><span class="factor-cancel">x</span>(x − 2)</div>
        </div>
        <span>=</span>
        <div class="frac">
          <div class="num">x + 4</div>
          <div class="den">x − 2</div>
        </div>
      </div>

      <div class="subtag subtag-do">Multiplied</div>
    </div>

    
    <div class="panel panel-dont">
      <div class="badge badge-dont">✕ Never Cancel Terms</div>
      
      <div class="math-row" id="mathDont">
        <div class="frac">
          <div class="num"><span class="term-error">x</span> + 4</div>
          <div class="den"><span class="term-error">x</span> − 2</div>
        </div>
        <span>≠</span>
        <div class="frac">
          <div class="num">+4</div>
          <div class="den">−2</div>
        </div>
      </div>

      <div class="subtag subtag-dont">Added / Subtracted</div>
    </div>
  </div>

  <button class="toggle-btn" id="numToggle" onclick="toggleTest()">Test with x = 6</button>

  <script>
    let isTesting = false;

    function toggleTest() {
      isTesting = !isTesting;
      const btn = document.getElementById('numToggle');
      const mathDo = document.getElementById('mathDo');
      const mathDont = document.getElementById('mathDont');

      if (isTesting) {
        btn.textContent = 'Show Variables';
        btn.style.borderColor = '#22b7ff';
        
        mathDo.innerHTML = `
          <div class="frac">
            <div class="num"><span class="factor-cancel">6</span>(10)</div>
            <div class="den"><span class="factor-cancel">6</span>(4)</div>
          </div>
          <span>=</span>
          <div class="frac">
            <div class="num">10</div>
            <div class="den">4</div>
          </div>
          <span>= 2.5 ✓</span>
        `;

        mathDont.innerHTML = `
          <div class="frac">
            <div class="num">6 + 4</div>
            <div class="den">6 − 2</div>
          </div>
          <span>=</span>
          <div class="frac">
            <div class="num">10</div>
            <div class="den">4</div>
          </div>
          <span>≠ −2 ✕</span>
        `;
      } else {
        btn.textContent = 'Test with x = 6';
        btn.style.borderColor = '#cbd5e1';

        mathDo.innerHTML = `
          <div class="frac">
            <div class="num"><span class="factor-cancel">x</span>(x + 4)</div>
            <div class="den"><span class="factor-cancel">x</span>(x − 2)</div>
          </div>
          <span>=</span>
          <div class="frac">
            <div class="num">x + 4</div>
            <div class="den">x − 2</div>
          </div>
        `;

        mathDont.innerHTML = `
          <div class="frac">
            <div class="num"><span class="term-error">x</span> + 4</div>
            <div class="den"><span class="term-error">x</span> − 2</div>
          </div>
          <span>≠</span>
          <div class="frac">
            <div class="num">+4</div>
            <div class="den">−2</div>
          </div>
        `;
      }
    }
  </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;
      color: #1e2945;
      background: #ffffff;
      padding: 12px;
      display: flex;
      flex-direction: column;
      gap: 10px;
    }

    .column-selector {
      display: flex;
      justify-content: center;
      gap: 6px;
      flex-wrap: wrap;
    }
    .col-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      border-radius: 6px;
      padding: 4px 10px;
      font-size: 13px;
      font-weight: 600;
      color: #475569;
      cursor: pointer;
      transition: all 0.2s ease;
    }
    .col-btn.active {
      background: #0284c7;
      color: #ffffff;
      border-color: #0284c7;
    }

    .comparison {
      display: grid;
      grid-template-columns: 1fr 1.35fr;
      gap: 12px;
      align-items: start;
    }
    @media (max-width: 520px) {
      .comparison {
        grid-template-columns: 1fr;
      }
    }

    .panel {
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 8px;
      padding: 10px 12px;
    }
    .panel.wrong {
      border-color: #fca5a5;
      background: #fef2f2;
    }
    .panel.correct {
      border-color: #86efac;
      background: #f0fdf4;
    }

    .panel-header {
      display: flex;
      align-items: center;
      justify-content: space-between;
      font-size: 13px;
      font-weight: 700;
      margin-bottom: 8px;
      padding-bottom: 4px;
      border-bottom: 1px dashed rgba(0,0,0,0.1);
    }
    .badge-wrong { color: #dc2626; }
    .badge-correct { color: #16a34a; }

    .math-table {
      font-family: "Courier New", Courier, monospace;
      font-size: 13.5px;
      line-height: 1.4;
      white-space: pre;
    }

    /* Column Alignment Matrix */
    .grid-div {
      display: grid;
      grid-template-columns: auto repeat(4, minmax(28px, 1fr));
      font-family: "Courier New", Courier, monospace;
      font-size: 13.5px;
      line-height: 1.35;
      text-align: right;
    }
    .cell {
      padding: 1px 2px;
      transition: background-color 0.2s ease, color 0.2s ease;
      border-radius: 3px;
    }
    .bracket-top {
      border-top: 1.5px solid #1e2945;
    }
    .bracket-left {
      border-left: 1.5px solid #1e2945;
      border-top-left-radius: 4px;
      padding-left: 4px;
    }
    .sub-line {
      border-bottom: 1px solid #64748b;
    }
    .text-divisor {
      text-align: right;
      padding-right: 4px;
      color: #334155;
    }

    .col-header {
      font-size: 11px;
      font-weight: 700;
      color: #64748b;
      text-align: right;
      padding-bottom: 2px;
      border-bottom: 1px solid #cbd5e1;
      margin-bottom: 2px;
    }

    /* Highlight classes */
    .hl-0 { background: #e0f2fe; color: #0369a1; font-weight: bold; }
    .hl-1 { background: #fef08a; color: #854d0e; font-weight: bold; }
    .hl-2 { background: #bbf7d0; color: #15803d; font-weight: bold; }
    .hl-3 { background: #fed7aa; color: #9a3412; font-weight: bold; }

    .clash-box {
      margin-top: 8px;
      padding: 6px;
      background: #fee2e2;
      border: 1px dashed #ef4444;
      border-radius: 6px;
      font-size: 12px;
      color: #991b1b;
      font-weight: 600;
      text-align: center;
    }

    .placeholder-pill {
      background: #dcfce7;
      color: #15803d;
      font-weight: 700;
      border-radius: 3px;
      padding: 0 2px;
    }
  </style>
</head>
<body>

  
  <div class="column-selector">
    <button class="col-btn active" data-col="all">All Columns</button>
    <button class="col-btn" data-col="0">x³</button>
    <button class="col-btn" data-col="1">x² (0x²)</button>
    <button class="col-btn" data-col="2">x (0x)</button>
    <button class="col-btn" data-col="3">Constants</button>
  </div>

  <div class="comparison">
    
    <div class="panel wrong">
      <div class="panel-header badge-wrong">
        <span>Without Placeholders</span>
        <span>✕</span>
      </div>

      <div class="math-table">
        x²
    ┌───────
x-2 │ x³    - 8
   -(x³ - 2x²)
   ───────────
      <span style="color:#dc2626; font-weight:bold;">-8 - (-2x²) = ?</span>
      </div>

      <div class="clash-box">
        ⚠️ Misaligned: constant vs x²
      </div>
    </div>

    
    <div class="panel correct">
      <div class="panel-header badge-correct">
        <span>With Placeholders</span>
        <span>✓</span>
      </div>

      <div class="grid-div">
        
        <div class="col-header"></div>
        <div class="col-header c-0">x³</div>
        <div class="col-header c-1">x²</div>
        <div class="col-header c-2">x</div>
        <div class="col-header c-3">const</div>

        
        <div></div>
        <div class="cell c-0">x²</div>
        <div class="cell c-1">+2x</div>
        <div class="cell c-2">+4</div>
        <div class="cell c-3"></div>

        
        <div class="text-divisor">x-2</div>
        <div class="cell c-0 bracket-top bracket-left">x³</div>
        <div class="cell c-1 bracket-top"><span class="placeholder-pill">+0x²</span></div>
        <div class="cell c-2 bracket-top"><span class="placeholder-pill">+0x</span></div>
        <div class="cell c-3 bracket-top">-8</div>

        
        <div class="text-divisor">-</div>
        <div class="cell c-0 sub-line">(x³</div>
        <div class="cell c-1 sub-line">-2x²)</div>
        <div class="cell c-2 sub-line"></div>
        <div class="cell c-3 sub-line"></div>

        
        <div></div>
        <div class="cell c-0"></div>
        <div class="cell c-1">2x²</div>
        <div class="cell c-2">+0x</div>
        <div class="cell c-3"></div>

        
        <div class="text-divisor">-</div>
        <div class="cell c-0"></div>
        <div class="cell c-1 sub-line">(2x²</div>
        <div class="cell c-2 sub-line">-4x)</div>
        <div class="cell c-3 sub-line"></div>

        
        <div></div>
        <div class="cell c-0"></div>
        <div class="cell c-1"></div>
        <div class="cell c-2">4x</div>
        <div class="cell c-3">-8</div>

        
        <div class="text-divisor">-</div>
        <div class="cell c-0"></div>
        <div class="cell c-1"></div>
        <div class="cell c-2 sub-line">(4x</div>
        <div class="cell c-3 sub-line">-8)</div>

        
        <div></div>
        <div class="cell c-0"></div>
        <div class="cell c-1"></div>
        <div class="cell c-2"></div>
        <div class="cell c-3" style="font-weight: bold; color: #16a34a;">0</div>
      </div>
    </div>
  </div>

  <script>
    const buttons = document.querySelectorAll('.col-btn');
    const cells = document.querySelectorAll('.grid-div .cell, .grid-div .col-header');

    function highlightColumn(colIdx) {
      cells.forEach(cell => {
        cell.classList.remove('hl-0', 'hl-1', 'hl-2', 'hl-3');
      });

      if (colIdx === 'all') return;

      const targetClass = 'c-' + colIdx;
      const hlClass = 'hl-' + colIdx;

      document.querySelectorAll('.' + targetClass).forEach(cell => {
        cell.classList.add(hlClass);
      });
    }

    buttons.forEach(btn => {
      btn.addEventListener('click', () => {
        buttons.forEach(b => b.classList.remove('active'));
        btn.classList.add('active');
        highlightColumn(btn.dataset.col);
      });
    });
  </script>
</body>
</html>

Polynomial Long Division with Linear Divisors

Polynomial Long Division with Quadratic Divisors

Synthetic Division for Linear Divisors

The Polynomial Remainder Theorem

The Factor Theorem and Verifying Linear Factors

Finding Unknown Coefficients Using Remainder and Factor Theorems

Using the Rational Root Theorem to Find Possible Roots

Factoring Cubic and Quartic Polynomials Completely

Factoring Using Sum and Difference of Cubes

math

Polynomial Theorems, Division, and Advanced Factoring

Multiplying and Dividing Rational Expressions

Adding and Subtracting Rational Expressions with Unlike Denominators

Simplifying Complex Compound Fractions

Solving Rational Equations with Polynomial Denominators

Rational Expressions and Algebraic Fractions

Expressing Fractions with Linear Factors as Partial Fractions

Partial Fractions with Distinct Linear Denominators (ax+b)(cx+d)

Partial Fractions with Three or More Linear Factors

Partial Fractions with Repeated Linear Factors

Partial Fractions with a Quadratic Factor in the Denominator

Improper Rational Fractions and Preliminary Division

Partial Fraction Decomposition

□や△から文字へ — aやxの導入

加減の関係を文字式で表す — x + a と x - a

乗除の関係を文字式で表す — x × a と x ÷ a

文字に数を代入して式の値を求める

文字式が表す場面の読み取りと説明

文字を使った等式と逆算 — x に当てはまる数を求める

文字式を生活に活かす

文字を使った式 — xやaで数量の関係を表す

Expanding and Simplifying Polynomial Products

Polynomial Division by Linear Divisors

The Factor Theorem and Cubic Factorisation

Solving Cubic and Quartic Equations Algebraically

The Remainder Theorem and Unknown Coefficients

Sketching Polynomial Graphs from Factored Form

Simplifying Rational Expressions by Factorising

Simplifying Rational Expressions with Algebraic Division

Adding and Subtracting Algebraic Fractions

Polynomials and Algebraic Division

数学活動を通じて日常の現象を捉える

数学の学習から問題を見つけて解く

数と計算の体系的な振り返り — 整数・小数・分数の一貫性

図形の性質と計量の統合的振り返り

関数的思考の振り返り — 比例・反比例・文字式から中学数学へ

数学的な根拠をもった説明と対話的な学び合い

算数から数学への旅立ち — 数の世界の広がりと論理の力

算数の総合探究 — 数学的活動と学びの振り返り

OGM.12.ALG.1

OGM.12.ALG.1

Aligned learning resources

Related diagrams