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Multiplying and dividing rational expressions worksheets Grade 9

Factor everything, flip to divide, cancel, then multiply.

The front of the free multiplying and dividing rational expressions worksheet
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Free · Worked example · 17 problems · Answer key · US Letter

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How to do it

Factor everything. To divide, flip the second fraction. Cancel, then multiply.

x2−14x+48x+5×x+5x2−5x−24=(x−8)(x−6)x+5×x+5(x−8)(x+3)\dfrac{x^{2} - 14x + 48}{x + 5} \times \dfrac{x + 5}{x^{2} - 5x - 24} = \dfrac{(x - 8)(x - 6)}{x + 5} \times \dfrac{x + 5}{(x - 8)(x + 3)}factor everything
(x−8)(x−6)(x+5)(x+5)(x−8)(x+3)=x−6x+3\dfrac{(x - 8)(x - 6)(x + 5)}{(x + 5)(x - 8)(x + 3)} = \dfrac{x - 6}{x + 3}cancel (x − 8) and (x + 5)

Example problems

  1. x2−10x+9x+7×x+7x2−17x+72=\dfrac{x^{2} - 10x + 9}{x + 7} \times \dfrac{x + 7}{x^{2} - 17x + 72} =
  2. x2−3x+2x−9÷x−2x+8=\dfrac{x^{2} - 3x + 2}{x - 9} \div \dfrac{x - 2}{x + 8} =
  3. x2−9x+8x−5÷x−1x−9=\dfrac{x^{2} - 9x + 8}{x - 5} \div \dfrac{x - 1}{x - 9} =
  4. x2−14x+48x−5÷x−8x+9=\dfrac{x^{2} - 14x + 48}{x - 5} \div \dfrac{x - 8}{x + 9} =

Radicals, quadratics and rational expressions

  1. Simplifying square roots
  2. Adding and multiplying radicals
  3. Solving quadratic equations by factoring
  4. Completing the square
  5. The quadratic formula
  6. Simplifying rational expressions
  7. Multiplying and dividing rational expressions