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Simplifying rational expressions worksheets Grade 9

Factor the numerator and denominator, then cancel common factors.

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Free · Worked example · 34 problems · Answer key · US Letter

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How to do it

Factor the numerator and denominator, then cancel common factors.

3x2+9x−84x2−5x+4=3(x−4)(x+7)(x−4)(x−1)=3(x+7)x−1\dfrac{3x^{2} + 9x - 84}{x^{2} - 5x + 4} = \dfrac{3(x - 4)(x + 7)}{(x - 4)(x - 1)} = \dfrac{3(x + 7)}{x - 1}factor, then cancel (x − 4)

Example problems

  1. x2+6x−16x2−6x+8=\dfrac{x^{2} + 6x - 16}{x^{2} - 6x + 8} =
  2. 2x2−24x+54x2−15x+54=\dfrac{2x^{2} - 24x + 54}{x^{2} - 15x + 54} =
  3. 3x2−33x+72x2−15x+56=\dfrac{3x^{2} - 33x + 72}{x^{2} - 15x + 56} =
  4. x2+5x+4x2+7x+12=\dfrac{x^{2} + 5x + 4}{x^{2} + 7x + 12} =

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