To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x+y\right)\left(-x+y\right)$ and $\left(x+y\right)\left(x-y\right)$ is $\left(x+y\right)\left(-x+y\right)$. Multiply $\frac{y^{2}}{\left(x+y\right)\left(x-y\right)}$ times $\frac{-1}{-1}$.
Since $\frac{xy}{\left(x+y\right)\left(-x+y\right)}$ and $\frac{-y^{2}}{\left(x+y\right)\left(-x+y\right)}$ have the same denominator, subtract them by subtracting their numerators.
