To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(3m+n\right)\left(3m-n\right)$ and $3m+n$ is $\left(3m+n\right)\left(3m-n\right)$. Multiply $\frac{3m-n}{3m+n}$ times $\frac{3m-n}{3m-n}$.
Since $\frac{9m^{2}+n^{2}}{\left(3m+n\right)\left(3m-n\right)}$ and $\frac{\left(3m-n\right)\left(3m-n\right)}{\left(3m+n\right)\left(3m-n\right)}$ have the same denominator, subtract them by subtracting their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(3m+n\right)\left(3m-n\right)$ and $3m+n$ is $\left(3m+n\right)\left(3m-n\right)$. Multiply $\frac{3m-n}{3m+n}$ times $\frac{3m-n}{3m-n}$.
Since $\frac{9m^{2}+n^{2}}{\left(3m+n\right)\left(3m-n\right)}$ and $\frac{\left(3m-n\right)\left(3m-n\right)}{\left(3m+n\right)\left(3m-n\right)}$ have the same denominator, subtract them by subtracting their numerators.
