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