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JAMB 1989 · UME · Q26

Express 1x+1−1x−2\dfrac{1}{x + 1} - \dfrac{1}{x - 2} as a single fraction.

Worked solution (try it first)
  1. Over the LCD (x+1)(x−2)(x + 1)(x - 2) the top is (x−2)−(x+1)=−3(x - 2) - (x + 1) = -3.
  2. So the fraction is −3(x+1)(x−2)\frac{-3}{(x + 1)(x - 2)}.
  3. The options use 2−x2 - x, and x−2=−(2−x)x - 2 = -(2 - x).
  4. Swapping the bracket cancels the minus: 3(x+1)(2−x)\dfrac{3}{(x + 1)(2 - x)}, option B.

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