\(\frac{1}{p}\) - \(\frac{1}{q}\) \(\div\) \(\frac{p}{q}\) - \(\frac{q}{p}\) = \(\frac{q - p}{pq}\) \div \(\frac{p^2 - q^2}{pq}\) \(\frac{q - p}{pq}\) x \(\frac{pq}{p^2q^2}\) = \(\frac{q - p}{p^2 - q^2}\) \(\frac{-(p - q)}{(p + q)(p - q)}\) = \(\frac{-1}{p + q}\)