Adding and subtracting rational expressions

Lessons

• Introduction
  review – adding/subtracting fractions

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• 1.
  Simplify:
  a)

  $\frac{3}{{13}} + \frac{8}{{13}}$
  
  
  b)

  $\frac{3}{2} + \frac{4}{5}$
  
  

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• 2.
  Simplify:
  a)

  $\frac{x}{6} + \frac{{2x}}{3} - \frac{{5x}}{4}$
  
  
  b)

  $\frac{{y - 3}}{3} + \frac{{2y + 3}}{6}$
  
  
  c)

  $\frac{{3a - 5}}{3} - \frac{{2a - 1}}{2}$
  
  

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• 3.
  Simplify:
  a)

  $\frac{{5x - 3}}{9} + 6x - \frac{{3x - 2}}{3}$
  
  
  b)

  $3 - \frac{{y - 1}}{4} - \frac{{4 - 3y}}{6}$
  
  

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• 4.
  Adding and Subtracting with Common Denominators
  State any restrictions on the variables, then simplify:
  a)

  $\frac{3}{x} + \frac{{12}}{x} - \frac{5}{x}$
  
  
  b)

  $\frac{{6a - 2}}{{3a}} + \frac{{ - 10a + 2}}{{3a}}$
  
  
  c)

  $\frac{{6m}}{{6m - 5}} - \frac{5}{{6m - 5}}$
  
  
  d)

  $\frac{{9x - 1}}{{2x - 3}} - \frac{{8 + 3x}}{{2x - 3}}$
  
  

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• 5.
  Adding and Subtracting with Different Monomial Denominators
  State any restrictions on the variables, then simplify:
  a)

  $\frac{3}{{4m}} + \frac{2}{{5m}}$
  
  
  b)

  $\frac{5}{{4x}} - \frac{7}{6}$
  
  
  c)

  $\frac{{2x - 3}}{{10x}} - \frac{{3x - 2}}{{5x}}$
  
  
  d)

  $\frac{{y - 1}}{{3y}} - \frac{2}{{2{y^2}}}$
  
  

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• 6.
  Adding and Subtracting with Different Monomial/Binomial Denominators
  State any restrictions on the variables, then simplify:
  a)

  $\frac{{x - 4}}{{3x}} + \frac{{5x}}{{x - 2}}$
  
  
  b)

  $\frac{5}{{3m + 2}} - \frac{1}{{4m - 7}}$
  
  
  c)

  $\frac{6x-1}{2x+3}-\frac{1-x}{4x+5}$
  
  

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• 7.
  State any restrictions on the variables, then simplify: $\frac{1}{{x + 2}} - \frac{5}{{x - 1}} + \frac{3}{x}$

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• 8.
  Denominators with Factors in Common
  State any restrictions on the variables, then simplify:
  a)

  $\frac{5}{{4x}} - \frac{5}{{12x}}$
  
  
  b)

  $\frac{4}{{3x + 9}} + \frac{5}{{2x + 6}}$
  
  
  c)

  $\frac{3}{{{x^2} - 5x}} - \frac{8}{{{x^2}}}$
  
  

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• 9.
  Denominators with Factors in Common
  State any restrictions on the variables, then simplify: $\frac{5}{{\left( {x - 1} \right)\left( {x + 3} \right)}} + \frac{4}{{\left( {x + 2} \right)\left( {x - 1} \right)}}$

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• 10.
  State any restrictions on the variables, then simplify: $\frac{x}{{{x^2} - 9}} + \frac{5}{{x - 3}}$

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• 11.
  State any restrictions on the variables, then simplify:
  a)

  $\frac{4}{{x - 3}} - \frac{{5 - x}}{{{x^2} - 2x - 3}}$
  
  
  b)

  $\frac{3}{{{a^2} - a - 2}} + \frac{5}{{{a^2} + 3a + 2}}$
  
  
  c)

  $\frac{1}{{{x^2} + 4x + 4}} - \frac{4}{{{x^2} + 5x + 6}}$
  
  

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• 12.
  State any restrictions on the variables, then simplify: $\frac{{{x^2} - 5x + 6}}{{{x^2} - 2x - 3}} - \frac{{{x^2} + 9x + 20}}{{{x^2} + 7x + 10}}$

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