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JAMB 1991 · UME · Q11

Simplify 13+5−13−5\dfrac{1}{3 + \sqrt5} - \dfrac{1}{3 - \sqrt5}.

Worked solution (try it first)
  1. Use the common denominator (3+5)(3−5)=9−5(3 + \sqrt5)(3 - \sqrt5) = 9 - 5, which is 4.
  2. The top is (3−5)−(3+5)=−25(3 - \sqrt5) - (3 + \sqrt5) = -2\sqrt5.
  3. So the value is −254=−125\dfrac{-2\sqrt5}{4} = -\frac12\sqrt5, option A.

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