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