Answer
$$=\frac{p^3}{p^2+q^2}$$
Work Step by Step
Simplifying using the rules of fractions, we find:
$$p-\frac{pq^2}{p^2+q^2} \\ -\frac{pq^2}{p^2+q^2}+\frac{p\left(p^2+q^2\right)}{p^2+q^2} \\ \frac{-pq^2+p\left(p^2+q^2\right)}{p^2+q^2} \\ =\frac{p^3}{p^2+q^2}$$
