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