Answer
$ \frac{x^2}{y^2}$.
Work Step by Step
The given expression is
$=\frac{\frac{x}{y^2}+\frac{1}{y}}{\frac{y}{x^2}+\frac{1}{x}}$
The LCD of all denominators is $x^2y^2$.
Multiply the numerator and the denominator by $x^2y^2$
$=\frac{x^2y^2}{x^2y^2}\cdot \frac{\frac{x}{y^2}+\frac{1}{y}}{\frac{y}{x^2}+\frac{1}{x}}$
Use the distributive property.
$= \frac{x^2y^2\cdot \frac{x}{y^2}+x^2y^2\cdot\frac{1}{y}}{x^2y^2\cdot\frac{y}{x^2}+x^2y^2\cdot\frac{1}{x}}$
Clear common terms.
$= \frac{x^3+x^2y}{y^3+xy^2}$
Factor the numerator and the denominator.
$= \frac{x^2(x+y)}{y^2(y+x)}$
Clear common terms.
$= \frac{x^2}{y^2}$.
