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NECO 2022 · Paper 1 · Q21

Simplify a2−4a2−a−6\dfrac{a^2 - 4}{a^2 - a - 6}.

Worked solution (try it first)
  1. Factorise the top as a difference of two squares: a2−4=(a−2)(a+2)a^2 - 4 = (a - 2)(a + 2).
  2. Factorise the bottom: a2−a−6=(a−3)(a+2)a^2 - a - 6 = (a - 3)(a + 2).
  3. Cancel the common factor (a+2)(a + 2): a−2a−3\dfrac{a - 2}{a - 3}, option E.

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