$$\frac { x } { x + y } - \frac { x y } { x ^ { 2 } + 2 x y + y ^ { 2 } }$$
Evaluate
$\left(\frac{x}{x+y}\right)^{2}$
Short Solution Steps
Factor $x^{2}+2xy+y^{2}$.
$$\frac{x}{x+y}-\frac{xy}{\left(x+y\right)^{2}}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x+y$ and $\left(x+y\right)^{2}$ is $\left(x+y\right)^{2}$. Multiply $\frac{x}{x+y}$ times $\frac{x+y}{x+y}$.
Since $\frac{x\left(x+y\right)}{\left(x+y\right)^{2}}$ and $\frac{xy}{\left(x+y\right)^{2}}$ have the same denominator, subtract them by subtracting their numerators.
