To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $2x+3y$ and $2x-3y$ is $\left(2x-3y\right)\left(2x+3y\right)$. Multiply $\frac{2x}{2x+3y}$ times $\frac{2x-3y}{2x-3y}$. Multiply $\frac{3y}{2x-3y}$ times $\frac{2x+3y}{2x+3y}$.
Since $\frac{2x\left(2x-3y\right)}{\left(2x-3y\right)\left(2x+3y\right)}$ and $\frac{3y\left(2x+3y\right)}{\left(2x-3y\right)\left(2x+3y\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{4x^{2}+9y^{2}}{\left(2x-3y\right)\left(2x+3y\right)}$ and $\frac{18y^{2}}{\left(2x-3y\right)\left(2x+3y\right)}$ have the same denominator, subtract them by subtracting their numerators.
