Answer
$\frac{x}{y}$.
Work Step by Step
The given expression is
$=\frac{x+\frac{1}{y}}{y+\frac{1}{x}}$
Multiply the numerator and the denominator by $xy$.
$=\frac{x+\frac{1}{y}}{y+\frac{1}{x}}\cdot \frac{xy}{xy}$
Use the distributive property.
$=\frac{x^2y+x}{xy^2+y}$
Factor the fraction.
$=\frac{x(xy+1)}{y(xy+1)}$
Cancel common terms.
$=\frac{x}{y}$.
