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Solving rational equations worksheets Grades 9–10

Multiply every term by the LCD, solve, and check for excluded values.

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Free · Worked example · 7 problems · Answer key · US Letter

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How to do it

Multiply every term by the LCD and solve. Check each answer: one that makes a denominator 0 is not a solution.

x2x−7=4x+21x−7x=−3\dfrac{x^{2}}{x - 7} = \dfrac{4x + 21}{x - 7}\quad x = -3
x2=4x+21x^{2} = 4x + 21multiply both sides by (x − 7)
x2−4x−21=0x^{2} - 4x - 21 = 0move every term to one side
(x−7)(x+3)=0(x - 7)(x + 3) = 0factor
x=7 or x=−3x = 7\ \text{or }x = -3set each factor equal to 0
x=7 makes the denominator 0, so it is not a solution.x = 7\ \text{makes the denominator }0,\ \text{so it is not a solution.}check each answer
x=−3x = -3

Example problems

  1. x2x−4=10x−24x−4\dfrac{x^{2}}{x - 4} = \dfrac{10x - 24}{x - 4}
  2. 2x+52x=34\dfrac{2}{x} + \dfrac{5}{2x} = \dfrac{3}{4}
  3. 8x+45x=1110\dfrac{8}{x} + \dfrac{4}{5x} = \dfrac{11}{10}
  4. 83x+56x=−716\dfrac{8}{3x} + \dfrac{5}{6x} = -\dfrac{7}{16}

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