в) \(\frac{p-q}{p+q}\) и \(\frac{p+q}{p-q}\);
Сумма:
\(\frac{p-q}{p+q} + \frac{p+q}{p-q} = \frac{(p-q) \cdot (p-q) + (p+q) \cdot (p+q)}{(p+q)(p-q)} = \frac{p^2-2pq+q^2 + p^2+2pq+q^2}{(p+q)(p-q)} = \frac{2p^2+2q^2}{(p+q)(p-q)} = \frac{2(p^2+q^2)}{p^2-q^2}\)
Разность:
\(\frac{p-q}{p+q} - \frac{p+q}{p-q} = \frac{(p-q) \cdot (p-q) - (p+q) \cdot (p+q)}{(p+q)(p-q)} = \frac{p^2-2pq+q^2 - (p^2+2pq+q^2)}{(p+q)(p-q)} = \frac{p^2-2pq+q^2 - p^2-2pq-q^2}{(p+q)(p-q)} = \frac{-4pq}{(p+q)(p-q)} = \frac{-4pq}{p^2-q^2}\)
Ответ: Сумма: \(\frac{2(p^2+q^2)}{p^2-q^2}\); Разность: \(\frac{-4pq}{p^2-q^2}\)