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 $\frac{a+b}{a-b}$ times $\frac{a+b}{a+b}$. Multiply $\frac{a-b}{a+b}$ times $\frac{a-b}{a-b}$.
Since $\frac{\left(a+b\right)\left(a+b\right)}{\left(a+b\right)\left(a-b\right)}$ and $\frac{\left(a-b\right)\left(a-b\right)}{\left(a+b\right)\left(a-b\right)}$ have the same denominator, subtract them by subtracting their numerators.
Multiply $\frac{4ab}{\left(a+b\right)\left(a-b\right)}$ times $\frac{a^{2}-b^{2}}{4ab}$ by multiplying numerator times numerator and denominator times denominator.
