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Simplifying complex fractions worksheets Grades 9–10

Multiply the top and bottom by the LCD of the small fractions, then simplify.

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Free · Worked example · 30 problems · Answer key · US Letter

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How to do it

Multiply the top and the bottom by the LCD of all the small fractions. Then simplify.

1x−18x−8=8−x8x(x−8)\dfrac{\dfrac{1}{x} - \dfrac{1}{8}}{x - 8} = \dfrac{8 - x}{8x(x - 8)}multiply the top and the bottom by 8x
8−x8x(x−8)=−(x−8)8x(x−8)=−18x\dfrac{8 - x}{8x(x - 8)} = \dfrac{-(x - 8)}{8x(x - 8)} = \dfrac{-1}{8x}8 − x = −(x − 8); cancel (x − 8)

Example problems

  1. x−1x1+1x=\dfrac{x - \dfrac{1}{x}}{1 + \dfrac{1}{x}} =
  2. x−16x1+4x=\dfrac{x - \dfrac{16}{x}}{1 + \dfrac{4}{x}} =
  3. x−16x1−4x=\dfrac{x - \dfrac{16}{x}}{1 - \dfrac{4}{x}} =
  4. 1+2x1−5x=\dfrac{1 + \dfrac{2}{x}}{1 - \dfrac{5}{x}} =

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