Stepwise
Start practisingPractise

JAMB 1993 · UME · Q19

Simplify 1p−1qpq−qp\dfrac{\frac1p - \frac1q}{\frac pq - \frac qp}.

Worked solution (try it first)
  1. Top: 1p−1q=q−ppq\frac1p - \frac1q = \frac{q - p}{pq}.
  2. Bottom: pq−qp=p2−q2pq\frac pq - \frac qp = \frac{p^2 - q^2}{pq}.
  3. Divide.
  4. The pqpq cancels: q−pp2−q2=−(p−q)(p−q)(p+q)\frac{q - p}{p^2 - q^2} = \frac{-(p - q)}{(p - q)(p + q)}.
  5. Cancel p−qp - q: the result is −1p+q-\dfrac{1}{p + q}, option B.

Report a problem with this question