3. Given $p q<0, p^{2}+q^{2}=p^{2} q^{2}$. Simplify $p \sqrt{1-\frac{1}{p^{2}}}-q \sqrt{1-\frac{1}{q^{2}}}$ and the result is ( ).
(A) $p q$ or $-p q$
(B) $p q$
(C) $-p q$
(D) 2
3. (A)

It is easy to know that $\frac{1}{p^{2}}+\frac{1}{q^{2}}=1$.
$$
\begin{aligned}
\text { Original expression } & =\frac{p}{|q|}-\frac{q}{|p|}=\frac{p|p|-q|q|}{|p q|} \\
& =-\frac{p|p|-q|q|}{p q} .
\end{aligned}
$$

When $p0>q$, the original expression $=-p q$.