<!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: #1e293b;
      background: #ffffff;
      padding: 12px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100vh;
      overflow-x: hidden;
    }

    .main-container {
      width: 100%;
      max-width: 580px;
      display: flex;
      flex-direction: column;
      gap: 12px;
      align-items: center;
    }

    /* Tab Buttons */
    .nav-tabs {
      display: flex;
      gap: 6px;
      width: 100%;
      justify-content: center;
      flex-wrap: wrap;
    }

    .tab-btn {
      padding: 6px 12px;
      font-size: 13px;
      font-weight: 600;
      border-radius: 18px;
      border: 1.5px solid #e2e8f0;
      background: #f8fafc;
      color: #64748b;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 5px;
      transition: background-color 0.2s ease, border-color 0.2s ease, color 0.2s ease;
      user-select: none;
      white-space: nowrap;
    }

    .tab-btn:hover {
      border-color: #cbd5e1;
      color: #1e293b;
      background: #f1f5f9;
    }

    .tab-btn.active {
      background: #1e293b;
      border-color: #1e293b;
      color: #ffffff;
    }

    /* Equation Card & Visual Canvas Area */
    .diagram-area {
      width: 100%;
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 12px;
      padding: 16px 10px 14px 10px;
      display: flex;
      flex-direction: column;
      align-items: center;
      position: relative;
    }

    .math-font {
      font-family: "KaTeX_Math", "Cambria Math", "Times New Roman", Times, serif;
      font-style: italic;
    }
    .math-normal {
      font-family: system-ui, -apple-system, sans-serif;
      font-style: normal;
    }

    /* Equation Layout */
    .eq-row {
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: clamp(15px, 4.4vw, 22px);
      white-space: nowrap;
      user-select: none;
      width: 100%;
    }

    .fraction-block {
      display: inline-flex;
      flex-direction: column;
      align-items: center;
      vertical-align: middle;
      padding: 0 2px;
      position: relative;
    }

    .frac-num, .frac-den {
      padding: 2px 5px;
      border-radius: 6px;
      transition: all 0.25s ease;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      line-height: 1.2;
    }

    .frac-bar {
      width: 100%;
      height: 2px;
      background: #334155;
      margin: 3px 0;
      border-radius: 1px;
    }

    .eq-op {
      padding: 0 clamp(3px, 1.5vw, 8px);
      font-weight: 500;
      color: #475569;
    }

    /* Targetable Factor Elements */
    .factor-item {
      padding: 1px 3px;
      border-radius: 5px;
      transition: all 0.25s ease;
      display: inline-block;
    }

    /* Anatomical Highlights */
    .hl-degree {
      background: #fef3c7 !important;
      box-shadow: 0 0 0 1.5px #d97706 !important;
      color: #92400e !important;
    }

    .hl-factorA {
      background: #e0f2fe !important;
      box-shadow: 0 0 0 1.5px #0284c7 !important;
      color: #0369a1 !important;
    }

    .hl-factorB {
      background: #fce7f3 !important;
      box-shadow: 0 0 0 1.5px #db2777 !important;
      color: #be185d !important;
    }

    /* Pointer / Connector Indicators Section */
    .indicators-container {
      width: 100%;
      margin-top: 14px;
      display: flex;
      flex-direction: column;
      gap: 8px;
    }

    .indicator-card {
      display: flex;
      align-items: center;
      justify-content: space-between;
      border-radius: 8px;
      padding: 7px 12px;
      font-size: clamp(11.5px, 3.2vw, 13px);
      font-weight: 500;
      transition: all 0.25s ease;
      opacity: 0.35;
      filter: grayscale(0.8);
      border: 1px dashed #cbd5e1;
      background: #ffffff;
    }

    .indicator-card.active {
      opacity: 1;
      filter: grayscale(0);
      font-weight: 600;
      transform: none;
    }

    .indicator-card.ind-deg.active {
      border: 1.5px solid #f59e0b;
      background: #fffbeb;
      color: #92400e;
    }

    .indicator-card.ind-a.active {
      border: 1.5px solid #0284c7;
      background: #f0f9ff;
      color: #0369a1;
    }

    .indicator-card.ind-b.active {
      border: 1.5px solid #db2777;
      background: #fdf2f8;
      color: #be185d;
    }

    .ind-label {
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .ind-badge {
      display: inline-flex;
      align-items: center;
      justify-content: center;
      padding: 2px 7px;
      border-radius: 12px;
      font-size: 11px;
      font-weight: 700;
    }

    .ind-badge-deg { background: #fde68a; color: #b45309; }
    .ind-badge-a { background: #bae6fd; color: #0284c7; }
    .ind-badge-b { background: #fbcfe8; color: #db2777; }

    .ind-target {
      display: flex;
      align-items: center;
      gap: 5px;
      font-family: "KaTeX_Math", "Cambria Math", "Times New Roman", serif;
      font-style: italic;
    }

    /* Explanation Callout */
    .callout-box {
      width: 100%;
      min-height: 84px;
      border-radius: 10px;
      padding: 12px 14px;
      display: flex;
      align-items: center;
      gap: 12px;
      transition: all 0.25s ease;
      border: 1.5px solid #e2e8f0;
      background: #f8fafc;
    }

    .callout-icon {
      font-size: 24px;
      line-height: 1;
      flex-shrink: 0;
    }

    .callout-content {
      display: flex;
      flex-direction: column;
      gap: 3px;
    }

    .callout-title {
      font-size: 14px;
      font-weight: 700;
      display: flex;
      align-items: center;
      gap: 6px;
    }

    .callout-desc {
      font-size: 12.5px;
      color: #475569;
      line-height: 1.35;
    }

    /* Theme colors */
    .theme-degree { background: #fffbeb; border-color: #fde68a; }
    .theme-degree .callout-title { color: #b45309; }

    .theme-factorA { background: #f0f9ff; border-color: #bae6fd; }
    .theme-factorA .callout-title { color: #0369a1; }

    .theme-factorB { background: #fdf2f8; border-color: #fbcfe8; }
    .theme-factorB .callout-title { color: #be185d; }

    .theme-all { background: #f8fafc; border-color: #cbd5e1; }
    .theme-all .callout-title { color: #1e293b; }

    @media (max-width: 380px) {
      .tab-btn { font-size: 11.5px; padding: 5px 8px; }
      .diagram-area { padding: 12px 6px 10px 6px; }
      .callout-box { padding: 10px 12px; gap: 8px; }
    }
  </style>
</head>
<body>

  <div class="main-container">
    
    <div class="nav-tabs">
      <button class="tab-btn active" onclick="setStage('degree')">1. Degree Check</button>
      <button class="tab-btn" onclick="setStage('factorA')">2. Factor (x - 2)</button>
      <button class="tab-btn" onclick="setStage('factorB')">3. Factor (x + 3)</button>
      <button class="tab-btn" onclick="setStage('all')">View All</button>
    </div>

    
    <div class="diagram-area">
      
      <div class="eq-row">
        
        <div class="fraction-block">
          <div id="lhs-num" class="frac-num">
            <span class="math-font">5x</span> <span class="math-normal">&minus;</span> <span class="math-normal">7</span>
          </div>
          <div class="frac-bar"></div>
          <div id="lhs-den" class="frac-den">
            <span id="k-denA" class="factor-item">(<span class="math-font">x</span> <span class="math-normal">&minus;</span> 2)</span>
            <span id="k-denB" class="factor-item">(<span class="math-font">x</span> <span class="math-normal">+</span> 3)</span>
          </div>
        </div>

        <span class="eq-op">&equals;</span>

        
        <div id="rhs-termA" class="fraction-block">
          <div id="rhs-numA" class="frac-num">
            <span class="math-font">A</span>
          </div>
          <div class="frac-bar"></div>
          <div id="rhs-denA" class="frac-den">
            <span class="math-font">x</span> <span class="math-normal">&minus;</span> 2
          </div>
        </div>

        <span class="eq-op">&plus;</span>

        
        <div id="rhs-termB" class="fraction-block">
          <div id="rhs-numB" class="frac-num">
            <span class="math-font">B</span>
          </div>
          <div class="frac-bar"></div>
          <div id="rhs-denB" class="frac-den">
            <span class="math-font">x</span> <span class="math-normal">+</span> 3
          </div>
        </div>
      </div>

      
      <div class="indicators-container">
        
        <div id="ind-degree" class="indicator-card ind-deg active">
          <div class="ind-label">
            <span class="ind-badge ind-badge-deg">Degree Test</span>
            <span>Numerator deg (1) &lt; Denominator deg (2)</span>
          </div>
          <span style="font-size: 11px; font-weight:700; color:#b45309;">PROPER FRACTION</span>
        </div>

        
        <div id="ind-factorA" class="indicator-card ind-a">
          <div class="ind-label">
            <span class="ind-badge ind-badge-a">Linear Factor 1</span>
            <span>(<span class="math-font">x</span> &minus; 2) in denominator</span>
          </div>
          <div class="ind-target">
            <span class="math-normal" style="font-size:12px;">&rarr; Needs Constant</span>
            <strong style="font-size:14px; color:#0284c7;">A</strong>
          </div>
        </div>

        
        <div id="ind-factorB" class="indicator-card ind-b">
          <div class="ind-label">
            <span class="ind-badge ind-badge-b">Linear Factor 2</span>
            <span>(<span class="math-font">x</span> + 3) in denominator</span>
          </div>
          <div class="ind-target">
            <span class="math-normal" style="font-size:12px;">&rarr; Needs Constant</span>
            <strong style="font-size:14px; color:#db2777;">B</strong>
          </div>
        </div>
      </div>
    </div>

    
    <div id="callout" class="callout-box theme-degree">
      <div id="callout-icon" class="callout-icon">⚖️</div>
      <div class="callout-content">
        <div id="callout-title" class="callout-title">Degree 1 &lt; Degree 2: Expression is Proper</div>
        <div id="callout-desc" class="callout-desc">The degree of numerator (1) is strictly less than denominator (2), so partial fractions decompose directly without polynomial division.</div>
      </div>
    </div>
  </div>

  <script>
    const stages = {
      degree: {
        highlights: {
          'lhs-num': 'hl-degree',
          'lhs-den': 'hl-degree'
        },
        indicators: ['ind-degree'],
        icon: '⚖️',
        title: 'Degree 1 < Degree 2: Expression is Proper',
        desc: 'Numerator degree (1) is less than denominator degree (2). The fraction is proper, so decompose directly without long division.',
        theme: 'theme-degree'
      },
      factorA: {
        highlights: {
          'k-denA': 'hl-factorA',
          'rhs-numA': 'hl-factorA',
          'rhs-denA': 'hl-factorA'
        },
        indicators: ['ind-factorA'],
        icon: '🔹',
        title: 'Linear Factor 1 → Needs Constant A',
        desc: 'The linear denominator factor (x - 2) produces a partial fraction term with a single undetermined constant A.',
        theme: 'theme-factorA'
      },
      factorB: {
        highlights: {
          'k-denB': 'hl-factorB',
          'rhs-numB': 'hl-factorB',
          'rhs-denB': 'hl-factorB'
        },
        indicators: ['ind-factorB'],
        icon: '🔸',
        title: 'Linear Factor 2 → Needs Constant B',
        desc: 'The second distinct linear factor (x + 3) creates the second partial fraction term with constant numerator B.',
        theme: 'theme-factorB'
      },
      all: {
        highlights: {
          'lhs-num': 'hl-degree',
          'k-denA': 'hl-factorA',
          'k-denB': 'hl-factorB',
          'rhs-numA': 'hl-factorA',
          'rhs-denA': 'hl-factorA',
          'rhs-numB': 'hl-factorB',
          'rhs-denB': 'hl-factorB'
        },
        indicators: ['ind-degree', 'ind-factorA', 'ind-factorB'],
        icon: '✨',
        title: 'Complete Partial Fraction Anatomy',
        desc: 'Each distinct linear factor in the denominator yields its own separate fraction with an unknown constant numerator (A and B).',
        theme: 'theme-all'
      }
    };

    function clearHighlights() {
      const allHighlightIds = ['lhs-num', 'lhs-den', 'k-denA', 'k-denB', 'rhs-numA', 'rhs-denA', 'rhs-numB', 'rhs-denB'];
      allHighlightIds.forEach(id => {
        const el = document.getElementById(id);
        if (el) el.classList.remove('hl-degree', 'hl-factorA', 'hl-factorB');
      });

      const allIndicators = ['ind-degree', 'ind-factorA', 'ind-factorB'];
      allIndicators.forEach(id => {
        const el = document.getElementById(id);
        if (el) el.classList.remove('active');
      });
    }

    function setStage(key) {
      // Update tab buttons
      const buttons = document.querySelectorAll('.tab-btn');
      buttons.forEach(btn => {
        btn.classList.toggle('active', btn.getAttribute('onclick').includes(`'${key}'`));
      });

      clearHighlights();

      const stage = stages[key];
      
      // Apply highlights
      Object.entries(stage.highlights).forEach(([id, cls]) => {
        const el = document.getElementById(id);
        if (el) el.classList.add(cls);
      });

      // Activate corresponding indicator rows
      stage.indicators.forEach(id => {
        const el = document.getElementById(id);
        if (el) el.classList.add('active');
      });

      // Update callout box
      const callout = document.getElementById('callout');
      callout.className = 'callout-box ' + stage.theme;
      document.getElementById('callout-icon').textContent = stage.icon;
      document.getElementById('callout-title').textContent = stage.title;
      document.getElementById('callout-desc').textContent = stage.desc;
    }

    // Initialize default stage
    setStage('degree');
  </script>
</body>
</html>

Expressing Fractions with Linear Factors as Partial Fractions

<!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, "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: 12px;
      user-select: none;
    }

    .nav-bar {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 5px;
      width: 100%;
      max-width: 520px;
      flex-wrap: wrap;
    }

    .step-btn {
      flex: 1;
      min-width: 80px;
      border: 1px solid #cbd5e1;
      background: #f8fafc;
      color: #475569;
      font-size: 12px;
      font-weight: 600;
      padding: 7px 4px;
      border-radius: 6px;
      cursor: pointer;
      text-align: center;
      transition: background-color 0.2s, color 0.2s, border-color 0.2s;
    }

    .step-btn:hover {
      background: #f1f5f9;
    }

    .step-btn.active {
      background: #0284c7;
      color: #ffffff;
      border-color: #0284c7;
    }

    .stage-container {
      position: relative;
      width: 100%;
      max-width: 520px;
      height: 270px;
      margin: 10px 0;
      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;
      gap: 12px;
      opacity: 0;
      visibility: hidden;
      transition: opacity 0.25s ease, visibility 0.25s ease;
      text-align: center;
      padding: 6px 12px;
    }

    .step-card.active {
      opacity: 1;
      visibility: visible;
    }

    .step-title {
      font-size: 13px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      color: #64748b;
    }

    /* Math typography styling */
    .math {
      font-family: "Cambria Math", "Latin Modern Math", "KaTeX_Main", "Times New Roman", serif;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      line-height: 1.2;
    }

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

    .math-main {
      font-size: 19px;
      color: #0f172a;
      flex-wrap: wrap;
      gap: 4px;
    }

    .math-sub {
      font-size: 16px;
      color: #334155;
      flex-wrap: wrap;
      gap: 4px;
    }

    .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      padding: 0 4px;
      line-height: 1;
    }

    .num {
      border-bottom: 1.5px solid currentColor;
      padding-bottom: 3px;
      margin-bottom: 2px;
    }

    .den {
      padding-top: 1px;
    }

    .frac-sm {
      font-size: 0.85em;
    }

    .badge-op {
      background: #e0f2fe;
      color: #0369a1;
      font-weight: 600;
      padding: 3px 10px;
      border-radius: 999px;
      font-size: 13px;
      display: inline-flex;
      align-items: center;
      gap: 4px;
    }

    .box-green {
      background: #ecfdf5;
      border: 2px solid #10b981;
      border-radius: 8px;
      padding: 6px 16px;
      color: #065f46;
      display: inline-flex;
      align-items: center;
      gap: 6px;
      font-size: 18px;
      font-weight: 700;
    }

    .box-purple {
      background: #faf5ff;
      border: 2px solid #a855f7;
      border-radius: 8px;
      padding: 6px 16px;
      color: #6b21a8;
      display: inline-flex;
      align-items: center;
      gap: 6px;
      font-size: 18px;
      font-weight: 700;
    }

    .box-final {
      background: #f0f9ff;
      border: 2px solid #0284c7;
      border-radius: 10px;
      padding: 10px 18px;
      color: #0369a1;
      font-size: 19px;
      font-weight: 700;
      box-shadow: 0 4px 12px rgba(2, 132, 199, 0.12);
      display: flex;
      align-items: center;
      gap: 8px;
      flex-wrap: wrap;
      justify-content: center;
    }

    .controls {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      width: 100%;
      max-width: 520px;
    }

    .ctrl-btn {
      background: #f1f5f9;
      border: 1px solid #cbd5e1;
      color: #334155;
      font-size: 13px;
      font-weight: 600;
      padding: 7px 14px;
      border-radius: 6px;
      cursor: pointer;
      display: flex;
      align-items: center;
      gap: 4px;
      min-width: 76px;
      justify-content: center;
      transition: background-color 0.2s;
    }

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

    .ctrl-play {
      background: #0284c7;
      border-color: #0284c7;
      color: #fff;
    }

    .ctrl-play:hover {
      background: #0369a1;
    }

    @media (max-width: 420px) {
      .step-btn {
        font-size: 11px;
        padding: 5px 2px;
        min-width: 60px;
      }
      .math-main {
        font-size: 16px;
      }
      .math-sub {
        font-size: 14px;
      }
      .box-green, .box-purple, .box-final {
        font-size: 16px;
        padding: 6px 12px;
      }
    }
  </style>
</head>
<body>

  <div class="nav-bar">
    <button class="step-btn active" onclick="goToStep(0)">1. Template</button>
    <button class="step-btn" onclick="goToStep(1)">2. Clear Frac</button>
    <button class="step-btn" onclick="goToStep(2)">3. Find A</button>
    <button class="step-btn" onclick="goToStep(3)">4. Find B</button>
    <button class="step-btn" onclick="goToStep(4)">5. Result</button>
  </div>

  <div class="stage-container">
    
    <div class="step-card active" id="card-0">
      <div class="step-title">Step 1: Write Template</div>
      <div class="math math-main">
        <div class="frac">
          <span class="num">5<span class="math-var">x</span> − 1</span>
          <span class="den">(<span class="math-var">x</span> − 3)(<span class="math-var">x</span> + 1)</span>
        </div>
        <span>=</span>
        <div class="frac">
          <span class="num"><span class="math-var">A</span></span>
          <span class="den"><span class="math-var">x</span> − 3</span>
        </div>
        <span>+</span>
        <div class="frac">
          <span class="num"><span class="math-var">B</span></span>
          <span class="den"><span class="math-var">x</span> + 1</span>
        </div>
      </div>
    </div>

    
    <div class="step-card" id="card-1">
      <div class="step-title">Step 2: Clear Fractions</div>
      <div class="badge-op">
        Multiply both sides by (<span class="math-var">x</span> − 3)(<span class="math-var">x</span> + 1)
      </div>
      <div class="math math-main" style="margin-top: 4px;">
        <span>5<span class="math-var">x</span> − 1 = <span class="math-var">A</span>(<span class="math-var">x</span> + 1) + <span class="math-var">B</span>(<span class="math-var">x</span> − 3)</span>
      </div>
    </div>

    
    <div class="step-card" id="card-2">
      <div class="step-title">Step 3: Test <span class="math-var">x</span> = 3 to isolate <span class="math-var">A</span></div>
      <div class="math math-sub">
        <span>5(3) − 1 = <span class="math-var">A</span>(3 + 1) + <span class="math-var">B</span>(0)</span>
      </div>
      <div class="math math-sub">
        <span>14 = 4<span class="math-var">A</span></span>
      </div>
      <div class="box-green math">
        <span><span class="math-var">A</span> = </span>
        <div class="frac">
          <span class="num">7</span>
          <span class="den">2</span>
        </div>
      </div>
    </div>

    
    <div class="step-card" id="card-3">
      <div class="step-title">Step 4: Test <span class="math-var">x</span> = −1 to isolate <span class="math-var">B</span></div>
      <div class="math math-sub">
        <span>5(−1) − 1 = <span class="math-var">A</span>(0) + <span class="math-var">B</span>(−1 − 3)</span>
      </div>
      <div class="math math-sub">
        <span>−6 = −4<span class="math-var">B</span></span>
      </div>
      <div class="box-purple math">
        <span><span class="math-var">B</span> = </span>
        <div class="frac">
          <span class="num">3</span>
          <span class="den">2</span>
        </div>
      </div>
    </div>

    
    <div class="step-card" id="card-4">
      <div class="step-title">Step 5: Final Decomposed Answer</div>
      <div class="math math-sub">
        <div class="frac">
          <span class="num">5<span class="math-var">x</span> − 1</span>
          <span class="den">(<span class="math-var">x</span> − 3)(<span class="math-var">x</span> + 1)</span>
        </div>
        <span>=</span>
      </div>
      <div class="box-final math">
        <div class="frac">
          <span class="num"><div class="frac frac-sm"><span class="num">7</span><span class="den">2</span></div></span>
          <span class="den"><span class="math-var">x</span> − 3</span>
        </div>
        <span>+</span>
        <div class="frac">
          <span class="num"><div class="frac frac-sm"><span class="num">3</span><span class="den">2</span></div></span>
          <span class="den"><span class="math-var">x</span> + 1</span>
        </div>
      </div>
    </div>
  </div>

  <div class="controls">
    <button class="ctrl-btn" id="prevBtn" onclick="prevStep()">← Prev</button>
    <button class="ctrl-btn ctrl-play" id="playBtn" onclick="togglePlay()">⏸ Pause</button>
    <button class="ctrl-btn" id="nextBtn" onclick="nextStep()">Next →</button>
  </div>

  <script>
    let currentStep = 0;
    const totalSteps = 5;
    let isPlaying = true;
    let timer = null;

    function renderStep(idx) {
      currentStep = (idx + totalSteps) % totalSteps;
      const navButtons = document.querySelectorAll('.step-btn');
      for (let i = 0; i < totalSteps; i++) {
        const btn = navButtons[i];
        const card = document.getElementById('card-' + i);
        if (i === currentStep) {
          btn.classList.add('active');
          card.classList.add('active');
        } else {
          btn.classList.remove('active');
          card.classList.remove('active');
        }
      }
    }

    function goToStep(idx) {
      renderStep(idx);
      resetAutoPlay();
    }

    function nextStep() {
      renderStep(currentStep + 1);
      resetAutoPlay();
    }

    function prevStep() {
      renderStep(currentStep - 1);
      resetAutoPlay();
    }

    function startTimer() {
      clearInterval(timer);
      timer = setInterval(() => {
        renderStep(currentStep + 1);
      }, 3500);
    }

    function resetAutoPlay() {
      if (isPlaying) {
        startTimer();
      }
    }

    function togglePlay() {
      isPlaying = !isPlaying;
      const playBtn = document.getElementById('playBtn');
      if (isPlaying) {
        playBtn.innerHTML = '⏸ Pause';
        startTimer();
      } else {
        playBtn.innerHTML = '▶ Play';
        clearInterval(timer);
      }
    }

    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">
  <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;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      padding: 12px;
      user-select: none;
    }

    .nav-tabs {
      display: flex;
      background: #f1f5f9;
      padding: 4px;
      border-radius: 12px;
      gap: 6px;
      margin-bottom: 16px;
      width: 100%;
      max-width: 380px;
    }

    .tab-btn {
      flex: 1;
      border: none;
      background: transparent;
      padding: 8px 12px;
      font-size: 14px;
      font-weight: 700;
      color: #64748b;
      border-radius: 8px;
      cursor: pointer;
      transition: all 0.25s ease;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 6px;
    }

    .tab-btn.active {
      background: #ffffff;
      color: #2563eb;
      box-shadow: 0 2px 6px rgba(0, 0, 0, 0.08);
    }

    .stage {
      width: 100%;
      max-width: 480px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 16px;
    }

    .expression-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 12px;
      font-size: 19px;
      font-weight: 600;
      flex-wrap: wrap;
    }

    .frac {
      display: inline-flex;
      flex-direction: column;
      vertical-align: middle;
      text-align: center;
      font-size: 18px;
      line-height: 1.15;
    }

    .num {
      border-bottom: 2px solid #1e2945;
      padding: 2px 6px;
    }

    .den {
      padding: 4px 6px 2px;
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 4px;
    }

    .factor {
      position: relative;
      display: inline-flex;
      align-items: center;
      justify-content: center;
      padding: 2px 6px;
      border-radius: 6px;
      transition: background 0.3s ease, color 0.3s ease;
    }

    .factor.highlight {
      background: #e0f2fe;
      color: #0369a1;
    }

    .factor.covered {
      color: transparent;
      background: #1e2945;
    }

    .cover-patch {
      position: absolute;
      inset: -3px;
      background: #1e2945;
      color: #ffffff;
      border-radius: 8px;
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 11px;
      font-weight: 700;
      gap: 4px;
      box-shadow: 0 4px 10px rgba(30, 41, 69, 0.25);
      animation: popIn 0.3s cubic-bezier(0.16, 1, 0.3, 1) forwards;
      z-index: 2;
    }

    @keyframes popIn {
      0% { transform: scale(0.85); opacity: 0; }
      100% { transform: scale(1); opacity: 1; }
    }

    .step-card {
      width: 100%;
      background: #f8fafc;
      border: 1px solid #e2e8f0;
      border-radius: 12px;
      padding: 14px 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      gap: 12px;
    }

    .calc-row {
      display: flex;
      align-items: center;
      justify-content: center;
      gap: 10px;
      font-size: 17px;
      font-weight: 600;
      flex-wrap: wrap;
    }

    .val-highlight {
      color: #2563eb;
      font-weight: 700;
    }

    .result-badge {
      background: #ecfdf5;
      border: 1px solid #a7f3d0;
      color: #047857;
      padding: 6px 16px;
      border-radius: 20px;
      font-size: 18px;
      font-weight: 800;
      display: inline-flex;
      align-items: center;
      gap: 6px;
    }

    .val-sub {
      background: #fef08a;
      padding: 0 3px;
      border-radius: 4px;
    }
  </style>
</head>
<body>

  <div class="nav-tabs">
    <button class="tab-btn active" id="tabA" onclick="setMode('A')">
      Solve for <i>A</i>
    </button>
    <button class="tab-btn" id="tabB" onclick="setMode('B')">
      Solve for <i>B</i>
    </button>
  </div>

  <div class="stage">
    
    <div class="expression-row">
      <div class="frac">
        <span class="num">5<span class="val-highlight">x</span> − 1</span>
        <span class="den">
          <span class="factor" id="factorA">
            (x − 3)
          </span>
          <span class="factor" id="factorB">
            (x + 1)
          </span>
        </span>
      </div>
    </div>

    
    <div class="step-card">
      <div class="calc-row" id="calcFlow">
        
      </div>
      <div class="result-badge" id="resultBadge">
        
      </div>
    </div>
  </div>

  <script>
    const factorA = document.getElementById('factorA');
    const factorB = document.getElementById('factorB');
    const tabA = document.getElementById('tabA');
    const tabB = document.getElementById('tabB');
    const calcFlow = document.getElementById('calcFlow');
    const resultBadge = document.getElementById('resultBadge');

    function setMode(mode) {
      if (mode === 'A') {
        tabA.classList.add('active');
        tabB.classList.remove('active');

        factorA.className = 'factor covered';
        factorA.innerHTML = '(x − 3)<div class="cover-patch">👆 (x−3)</div>';

        factorB.className = 'factor highlight';
        factorB.innerHTML = '(x + 1)';

        calcFlow.innerHTML = `
          <span>x = 3</span>
          <span>→</span>
          <div class="frac">
            <span class="num">5(<span class="val-sub">3</span>) − 1</span>
            <span class="den"><span class="val-sub">3</span> + 1</span>
          </div>
          <span>=</span>
          <div class="frac">
            <span class="num">14</span>
            <span class="den">4</span>
          </div>
        `;

        resultBadge.innerHTML = `<i>A</i> = <div class="frac" style="font-size:16px"><span class="num">7</span><span class="den">2</span></div>`;
      } else {
        tabB.classList.add('active');
        tabA.classList.remove('active');

        factorB.className = 'factor covered';
        factorB.innerHTML = '(x + 1)<div class="cover-patch">👆 (x+1)</div>';

        factorA.className = 'factor highlight';
        factorA.innerHTML = '(x − 3)';

        calcFlow.innerHTML = `
          <span>x = −1</span>
          <span>→</span>
          <div class="frac">
            <span class="num">5(<span class="val-sub">−1</span>) − 1</span>
            <span class="den"><span class="val-sub">−1</span> − 3</span>
          </div>
          <span>=</span>
          <div class="frac">
            <span class="num">−6</span>
            <span class="den">−4</span>
          </div>
        `;

        resultBadge.innerHTML = `<i>B</i> = <div class="frac" style="font-size:16px"><span class="num">3</span><span class="den">2</span></div>`;
      }
    }

    // Initial render
    setMode('A');
  </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">
  <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: #ffffff;
      padding: 16px;
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-height: 100%;
      gap: 16px;
    }

    .controls {
      display: flex;
      gap: 8px;
      background: #f1f5f9;
      padding: 4px;
      border-radius: 20px;
    }

    .tab-btn {
      border: none;
      background: transparent;
      padding: 6px 14px;
      font-size: 13px;
      font-weight: 600;
      color: #64748b;
      border-radius: 16px;
      cursor: pointer;
      transition: all 0.2s ease;
    }

    .tab-btn.active-blue {
      background: #2563eb;
      color: #ffffff;
      box-shadow: 0 2px 4px rgba(37, 99, 235, 0.25);
    }

    .tab-btn.active-orange {
      background: #ea580c;
      color: #ffffff;
      box-shadow: 0 2px 4px rgba(234, 88, 12, 0.25);
    }

    .tab-btn.active-both {
      background: #1e2945;
      color: #ffffff;
    }

    .cards-grid {
      display: flex;
      flex-direction: column;
      gap: 14px;
      width: 100%;
      max-width: 600px;
    }

    .op-card {
      background: #f8fafc;
      border: 1.5px solid #e2e8f0;
      border-radius: 14px;
      padding: 14px 16px;
      display: flex;
      flex-direction: column;
      gap: 12px;
      transition: opacity 0.3s ease, border-color 0.3s ease;
    }

    .op-card.dimmed {
      opacity: 0.35;
    }

    .op-card.active-card-blue {
      border-color: #93c5fd;
      background: #f0f7ff;
    }

    .op-card.active-card-orange {
      border-color: #fdba74;
      background: #fff7ed;
    }

    .header-row {
      display: flex;
      align-items: center;
      justify-content: space-between;
    }

    .badge {
      font-size: 12px;
      font-weight: 700;
      text-transform: uppercase;
      letter-spacing: 0.5px;
      padding: 3px 8px;
      border-radius: 6px;
    }

    .badge-blue {
      background: #dbeafe;
      color: #1d4ed8;
    }

    .badge-orange {
      background: #ffedd5;
      color: #c2410c;
    }

    .direction-label {
      font-size: 12px;
      font-weight: 600;
      color: #64748b;
    }

    .equation-flow {
      display: flex;
      align-items: center;
      justify-content: space-around;
      gap: 8px;
      overflow-x: auto;
      padding: 2px 0;
    }

    .math-block {
      display: flex;
      align-items: center;
      justify-content: center;
      font-size: 17px;
    }

    .arrow-container {
      display: flex;
      flex-direction: column;
      align-items: center;
      justify-content: center;
      min-width: 40px;
    }

    .arrow-icon {
      font-size: 20px;
      line-height: 1;
      font-weight: 900;
    }

    .arrow-blue {
      color: #2563eb;
    }

    .arrow-orange {
      color: #ea580c;
    }

    .katex {
      font-size: 1.05em !important;
    }
  </style>
</head>
<body>

  <div class="controls">
    <button class="tab-btn active-both" id="btnBoth">Both</button>
    <button class="tab-btn" id="btnCombine">Combine</button>
    <button class="tab-btn" id="btnDecompose">Decompose</button>
  </div>

  <div class="cards-grid">
    
    <div class="op-card active-card-blue" id="cardCombine">
      <div class="header-row">
        <span class="badge badge-blue">Combining</span>
        <span class="direction-label">Forward (Common Denominator)</span>
      </div>
      <div class="equation-flow">
        <div class="math-block" id="mathC1"></div>
        <div class="arrow-container arrow-blue">
          <span class="arrow-icon">→</span>
        </div>
        <div class="math-block" id="mathC2"></div>
      </div>
    </div>

    
    <div class="op-card active-card-orange" id="cardDecompose">
      <div class="header-row">
        <span class="badge badge-orange">Partial Fractions</span>
        <span class="direction-label">Reverse (Decomposition)</span>
      </div>
      <div class="equation-flow">
        <div class="math-block" id="mathD1"></div>
        <div class="arrow-container arrow-orange">
          <span class="arrow-icon">→</span>
        </div>
        <div class="math-block" id="mathD2"></div>
      </div>
    </div>
  </div>

  <script>
    function renderEquations() {
      if (window.katex) {
        katex.render(String.raw`\frac{2}{x-1} + \frac{3}{x+2}`, document.getElementById('mathC1'), { throwOnError: false });
        katex.render(String.raw`\frac{5x+1}{x^2+x-2}`, document.getElementById('mathC2'), { throwOnError: false });
        
        katex.render(String.raw`\frac{5x+1}{x^2+x-2}`, document.getElementById('mathD1'), { throwOnError: false });
        katex.render(String.raw`\frac{A}{x-1} + \frac{B}{x+2}`, document.getElementById('mathD2'), { throwOnError: false });
      } else {
        document.getElementById('mathC1').innerHTML = '2/(x-1) + 3/(x+2)';
        document.getElementById('mathC2').innerHTML = '(5x+1)/(x²+x-2)';
        document.getElementById('mathD1').innerHTML = '(5x+1)/(x²+x-2)';
        document.getElementById('mathD2').innerHTML = 'A/(x-1) + B/(x+2)';
      }
    }

    renderEquations();

    const btnBoth = document.getElementById('btnBoth');
    const btnCombine = document.getElementById('btnCombine');
    const btnDecompose = document.getElementById('btnDecompose');
    const cardCombine = document.getElementById('cardCombine');
    const cardDecompose = document.getElementById('cardDecompose');

    function setView(view) {
      btnBoth.className = 'tab-btn' + (view === 'both' ? ' active-both' : '');
      btnCombine.className = 'tab-btn' + (view === 'combine' ? ' active-blue' : '');
      btnDecompose.className = 'tab-btn' + (view === 'decompose' ? ' active-orange' : '');

      if (view === 'both') {
        cardCombine.classList.remove('dimmed');
        cardCombine.classList.add('active-card-blue');
        cardDecompose.classList.remove('dimmed');
        cardDecompose.classList.add('active-card-orange');
      } else if (view === 'combine') {
        cardCombine.classList.remove('dimmed');
        cardCombine.classList.add('active-card-blue');
        cardDecompose.classList.add('dimmed');
        cardDecompose.classList.remove('active-card-orange');
      } else if (view === 'decompose') {
        cardCombine.classList.add('dimmed');
        cardCombine.classList.remove('active-card-blue');
        cardDecompose.classList.remove('dimmed');
        cardDecompose.classList.add('active-card-orange');
      }
    }

    btnBoth.addEventListener('click', () => setView('both'));
    btnCombine.addEventListener('click', () => setView('combine'));
    btnDecompose.addEventListener('click', () => setView('decompose'));
  </script>
</body>
</html>

OGM.12.ALG.2

Aligned learning resources

Related diagrams