Simplify frac 1 p - frac 1 q frac p q - frac q p - JAMB Mathematics 1993 Question
Simplify \(\frac{1}{p}\) - \(\frac{1}{q}\) + \(\frac{p}{q}\) - \(\frac{q}{p}\)
A
\(\frac{1}{p - q}\)
B
\(\frac{-1}{p + q}\)
C
\(\frac{1}{pq}\)
D
\(\frac{1}{pq(p - q)}\)
correct option: b
\(\frac{1}{p}\) - \(\frac{1}{q}\) + \(\frac{p}{q}\) - \(\frac{q}{p}\) = \(\frac{q - p}{pq}\) + \(\frac{p^2 - q^2}{pq}\)
\(\frac{q - p}{pq}\) x \(\frac{pq}{p^2q^2}\) = \(\frac{q - p}{p^2 q^2}\)
\(\frac{-(p - q)}{(p + q)(p - q)}\)
= \(\frac{-1}{p + q}\)
\(\frac{q - p}{pq}\) x \(\frac{pq}{p^2q^2}\) = \(\frac{q - p}{p^2 q^2}\)
\(\frac{-(p - q)}{(p + q)(p - q)}\)
= \(\frac{-1}{p + q}\)
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