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Subtracting rational expressions with unlike denominators worksheets Grades 9–10

Rewrite over the LCD and subtract the whole second numerator.

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How to do it

Rewrite over the LCD. Subtract the whole second numerator: change the sign of every term in it.

6x−6−9x+5=6(x+5)(x−6)(x+5)−9(x−6)(x−6)(x+5)\dfrac{6}{x - 6} - \dfrac{9}{x + 5} = \dfrac{6(x + 5)}{(x - 6)(x + 5)} - \dfrac{9(x - 6)}{(x - 6)(x + 5)}rewrite each over the LCD, (x − 6)(x + 5)
6(x+5)−9(x−6)(x−6)(x+5)=−3x+84(x−6)(x+5)\dfrac{6(x + 5) - 9(x - 6)}{(x - 6)(x + 5)} = \dfrac{-3x + 84}{(x - 6)(x + 5)}subtract the whole second numerator, then combine like terms

Example problems

  1. 7x+5−7x−7=\dfrac{7}{x + 5} - \dfrac{7}{x - 7} =
  2. 94x−76x2=\dfrac{9}{4x} - \dfrac{7}{6x^{2}} =
  3. xx−6−2x−4=\dfrac{x}{x - 6} - \dfrac{2}{x - 4} =
  4. 2x−54x2=\dfrac{2}{x} - \dfrac{5}{4x^{2}} =

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