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