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NECO 2023 · Paper 1 · Q33

Simplify x2−8x+123(x2+x−6)×9(x+3)\dfrac{x^2 - 8x + 12}{3(x^2 + x - 6)} \times 9(x + 3).

Worked solution (try it first)
  1. Factorise: x2−8x+12=(x−2)(x−6)x^2 - 8x + 12 = (x - 2)(x - 6) and x2+x−6=(x+3)(x−2)x^2 + x - 6 = (x + 3)(x - 2).
  2. So the expression is (x−2)(x−6)3(x+3)(x−2)×9(x+3)\dfrac{(x - 2)(x - 6)}{3(x + 3)(x - 2)} \times 9(x + 3).
  3. Cancel x−2x - 2 and x+3x + 3, and divide 9 by 3.
  4. This leaves 3(x−6)3(x - 6), option D.

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