Adding and subtracting rational expressions

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Intros
Lessons
  1. review – adding/subtracting fractions
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Examples
Lessons
  1. Simplify:
    1. 313+813\frac{3}{{13}} + \frac{8}{{13}}
    2. 32+45\frac{3}{2} + \frac{4}{5}
  2. Simplify:
    1. x6+2x35x4\frac{x}{6} + \frac{{2x}}{3} - \frac{{5x}}{4}
    2. y33+2y+36\frac{{y - 3}}{3} + \frac{{2y + 3}}{6}
    3. 3a532a12\frac{{3a - 5}}{3} - \frac{{2a - 1}}{2}
  3. Simplify:
    1. 5x39+6x3x23\frac{{5x - 3}}{9} + 6x - \frac{{3x - 2}}{3}
    2. 3y1443y63 - \frac{{y - 1}}{4} - \frac{{4 - 3y}}{6}
  4. Adding and Subtracting with Common Denominators
    State any restrictions on the variables, then simplify:
    1. 3x+12x5x\frac{3}{x} + \frac{{12}}{x} - \frac{5}{x}
    2. 6a23a+10a+23a\frac{{6a - 2}}{{3a}} + \frac{{ - 10a + 2}}{{3a}}
    3. 6m6m556m5\frac{{6m}}{{6m - 5}} - \frac{5}{{6m - 5}}
    4. 9x12x38+3x2x3\frac{{9x - 1}}{{2x - 3}} - \frac{{8 + 3x}}{{2x - 3}}
  5. Adding and Subtracting with Different Monomial Denominators
    State any restrictions on the variables, then simplify:
    1. 34m+25m\frac{3}{{4m}} + \frac{2}{{5m}}
    2. 54x76\frac{5}{{4x}} - \frac{7}{6}
    3. 2x310x3x25x\frac{{2x - 3}}{{10x}} - \frac{{3x - 2}}{{5x}}
    4. y13y22y2\frac{{y - 1}}{{3y}} - \frac{2}{{2{y^2}}}
  6. Adding and Subtracting with Different Monomial/Binomial Denominators
    State any restrictions on the variables, then simplify:
    1. x43x+5xx2\frac{{x - 4}}{{3x}} + \frac{{5x}}{{x - 2}}
    2. 53m+214m7\frac{5}{{3m + 2}} - \frac{1}{{4m - 7}}
    3. 6x12x+31x4x+5 \frac{6x-1}{2x+3}-\frac{1-x}{4x+5}
  7. State any restrictions on the variables, then simplify: 1x+25x1+3x\frac{1}{{x + 2}} - \frac{5}{{x - 1}} + \frac{3}{x}
    1. Denominators with Factors in Common
      State any restrictions on the variables, then simplify:
      1. 54x512x\frac{5}{{4x}} - \frac{5}{{12x}}
      2. 43x+9+52x+6\frac{4}{{3x + 9}} + \frac{5}{{2x + 6}}
      3. 3x25x8x2\frac{3}{{{x^2} - 5x}} - \frac{8}{{{x^2}}}
    2. Denominators with Factors in Common
      State any restrictions on the variables, then simplify: 5(x1)(x+3)+4(x+2)(x1)\frac{5}{{\left( {x - 1} \right)\left( {x + 3} \right)}} + \frac{4}{{\left( {x + 2} \right)\left( {x - 1} \right)}}
      1. State any restrictions on the variables, then simplify: xx29+5x3\frac{x}{{{x^2} - 9}} + \frac{5}{{x - 3}}
        1. State any restrictions on the variables, then simplify:
          1. 4x35xx22x3\frac{4}{{x - 3}} - \frac{{5 - x}}{{{x^2} - 2x - 3}}
          2. 3a2a2+5a2+3a+2\frac{3}{{{a^2} - a - 2}} + \frac{5}{{{a^2} + 3a + 2}}
          3. 1x2+4x+44x2+5x+6\frac{1}{{{x^2} + 4x + 4}} - \frac{4}{{{x^2} + 5x + 6}}
        2. State any restrictions on the variables, then simplify: x25x+6x22x3x2+9x+20x2+7x+10\frac{{{x^2} - 5x + 6}}{{{x^2} - 2x - 3}} - \frac{{{x^2} + 9x + 20}}{{{x^2} + 7x + 10}}
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          Practice
          Topic Notes
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          When adding and subtracting rational expressions, the denominators of the expressions will dictate how we solve the questions. Different denominators in the expressions, for example, common denominators, different monomial/binomial denominators, and denominators with factors in common, will require different treatments. In addition, we need to keep in mind the restrictions on variables.