Cancel out $y-3$ in both numerator and denominator.
$$\frac{1}{y+3}+\frac{1}{y-3}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $y+3$ and $y-3$ is $\left(y-3\right)\left(y+3\right)$. Multiply $\frac{1}{y+3}$ times $\frac{y-3}{y-3}$. Multiply $\frac{1}{y-3}$ times $\frac{y+3}{y+3}$.
Since $\frac{y-3}{\left(y-3\right)\left(y+3\right)}$ and $\frac{y+3}{\left(y-3\right)\left(y+3\right)}$ have the same denominator, add them by adding their numerators.
Cancel out $y-3$ in both numerator and denominator.
$$\frac{1}{y+3}+\frac{1}{y-3}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $y+3$ and $y-3$ is $\left(y-3\right)\left(y+3\right)$. Multiply $\frac{1}{y+3}$ times $\frac{y-3}{y-3}$. Multiply $\frac{1}{y-3}$ times $\frac{y+3}{y+3}$.
Since $\frac{y-3}{\left(y-3\right)\left(y+3\right)}$ and $\frac{y+3}{\left(y-3\right)\left(y+3\right)}$ have the same denominator, add them by adding their numerators.
