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Adding rational expressions with unlike denominators worksheets Grades 9–10

Rewrite each fraction over the LCD and add.

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How to do it

Rewrite each fraction over the LCD, add the numerators, and combine like terms. Leave the denominator factored.

5x+4+5x−6=5(x−6)(x+4)(x−6)+5(x+4)(x+4)(x−6)\dfrac{5}{x + 4} + \dfrac{5}{x - 6} = \dfrac{5(x - 6)}{(x + 4)(x - 6)} + \dfrac{5(x + 4)}{(x + 4)(x - 6)}rewrite each over the LCD, (x + 4)(x − 6)
5(x−6)+5(x+4)(x+4)(x−6)=10x−10(x+4)(x−6)\dfrac{5(x - 6) + 5(x + 4)}{(x + 4)(x - 6)} = \dfrac{10x - 10}{(x + 4)(x - 6)}add the numerators, then combine like terms

Example problems

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

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