Answer
The simplified form of the rational expression $\frac{x}{x+y}\div \frac{y}{x+y}$ is$\frac{x}{y}$.
Work Step by Step
$\frac{x}{x+y}\div \frac{y}{x+y}$
$\frac{A}{B}\div \frac{C}{D}=\frac{A}{B}\cdot \frac{D}{C}$
The reciprocal of $\frac{y}{x+y}$ is$\frac{x+y}{y}$
So, multiply the reciprocal of the divisor,
$\begin{align}
& \frac{x}{x+y}\div \frac{y}{x+y}=\frac{x}{x+y}\cdot \frac{x+y}{y} \\
& =\frac{\left( x \right)\left( x+y \right)}{\left( x+y \right)\left( y \right)}
\end{align}$
Regroup and remove the factor equal to 1,
$\begin{align}
& \frac{x}{x+y}\div \frac{y}{x+y}=\frac{\left( x \right)\left( x+y \right)}{\left( x+y \right)\left( y \right)} \\
& =\frac{\left( x+y \right)\left( x \right)}{\left( x+y \right)\left( y \right)} \\
& =1\cdot \frac{\left( x \right)}{\left( y \right)} \\
& =\frac{x}{y}
\end{align}$
