JAMB - Mathematics (1993 - No. 18)
Simplify \(\frac{1}{p}\) - \(\frac{1}{q}\) \(\div\) \(\frac{p}{q}\) - \(\frac{q}{p}\)
\(\frac{1}{p - q}\)
\(\frac{-1}{p + q}\)
\(\frac{1}{pq}\)
\(\frac{1}{pq(p - q)}\)
Explicação
\(\frac{1}{p}\) - \(\frac{1}{q}\) \(\div\) \(\frac{p}{q}\) - \(\frac{q}{p}\) = \(\frac{q - p}{pq}\) ÷ \(\frac{p^2 - q^2}{pq}\)
\(\frac{q - p}{pq}\) 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 \(\frac{pq}{p^2q^2}\) = \(\frac{q - p}{p^2 - q^2}\)
\(\frac{-(p - q)}{(p + q)(p - q)}\)
= \(\frac{-1}{p + q}\)