Answer
$-1$
Work Step by Step
Multiply $\frac{rq}{rq}$ to the expression, we have:
$\frac{r^{-1}+q^{-1}}{r^{-1}-q^{-1}}\cdot \frac{r-q}{r+q}=\frac{rq}{rq}\cdot\frac{r^{-1}+q^{-1}}{r^{-1}-q^{-1}}\cdot \frac{r-q}{r+q}=\frac{q+r}{q-r}\cdot \frac{r-q}{r+q}=-1$
