Answer
$\dfrac{\dfrac{s}{r}+\dfrac{r}{s}}{\dfrac{s}{r}-\dfrac{r}{s}}=\dfrac{s^{2}+r^{2}}{(s-r)(s+r)}$
Work Step by Step
$\dfrac{\dfrac{s}{r}+\dfrac{r}{s}}{\dfrac{s}{r}-\dfrac{r}{s}}$
Evaluate the sum indicated in the numerator and the substraction indicated in the denominator:
$\dfrac{\dfrac{s}{r}+\dfrac{r}{s}}{\dfrac{s}{r}-\dfrac{r}{s}}=\dfrac{\dfrac{s^{2}+r^{2}}{rs}}{\dfrac{s^{2}-r^{2}}{rs}}=...$
Evaluate the division and simplify:
$...=\dfrac{s^{2}+r^{2}}{rs}\div\dfrac{s^{2}-r^{2}}{rs}=\dfrac{rs(s^{2}+r^{2})}{rs(s^{2}-r^{2})}=\dfrac{s^{2}+r^{2}}{s^{2}-r^{2}}=...$
Factor the denominator to provide a more simplified answer:
$...=\dfrac{s^{2}+r^{2}}{(s-r)(s+r)}$
