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Adding and subtracting rational expressions with like denominators worksheets Grades 9–10

Add or subtract the numerators over the same denominator, then simplify.

The front of the free adding and subtracting rational expressions with like denominators worksheet
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Free · Worked example · 34 problems · Answer key · US Letter

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How to do it

Add or subtract the numerators and keep the denominator. When subtracting, subtract the whole numerator. Simplify if you can.

6x+3x+8−5x−5x+8=6x+3−(5x−5)x+8=x+8x+8\dfrac{6x + 3}{x + 8} - \dfrac{5x - 5}{x + 8} = \dfrac{6x + 3 - (5x - 5)}{x + 8} = \dfrac{x + 8}{x + 8}subtract the whole second numerator
x+8x+8=(x+8)x+8=1\dfrac{x + 8}{x + 8} = \dfrac{(x + 8)}{x + 8} = 1factor the top, then cancel (x + 8)

Example problems

  1. 2x−4x−4−5x+5x−4=\dfrac{2x - 4}{x - 4} - \dfrac{5x + 5}{x - 4} =
  2. 5x−4x−3+3x+9x−3=\dfrac{5x - 4}{x - 3} + \dfrac{3x + 9}{x - 3} =
  3. 3x+6x+4−6x+8x+4=\dfrac{3x + 6}{x + 4} - \dfrac{6x + 8}{x + 4} =
  4. 6x−7x+7−2x+5x+7=\dfrac{6x - 7}{x + 7} - \dfrac{2x + 5}{x + 7} =

Rational expressions and equations

  1. Adding and subtracting rational expressions with like denominators
  2. Least common denominator of rational expressions
  3. Adding rational expressions with unlike denominators
  4. Subtracting rational expressions with unlike denominators
  5. Adding and subtracting rational expressions by factoring
  6. Simplifying complex fractions
  7. Solving rational proportions
  8. Solving rational equations