Answer
$\frac{y(y+x^{2})}{x(x+y^{2})}$
Work Step by Step
We multiply by $xy$, distribute, and simplify:
$\displaystyle \frac{x+\frac{y}{x}}{y+\frac{x}{y}}=\frac{xy(x+\frac{y}{x})}{xy(y+\frac{x}{y})}=\frac{x^{2}y+y^{2}}{xy^{2}+x^{2}}=\frac{y(y+x^{2})}{x(x+y^{2})}$
