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