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