Cancel out $x-3$ in both numerator and denominator.
$$\frac{x+3}{x^{2}+15}+\frac{1}{x-3}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x^{2}+15$ and $x-3$ is $\left(x-3\right)\left(x^{2}+15\right)$. Multiply $\frac{x+3}{x^{2}+15}$ times $\frac{x-3}{x-3}$. Multiply $\frac{1}{x-3}$ times $\frac{x^{2}+15}{x^{2}+15}$.
Since $\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+15\right)}$ and $\frac{x^{2}+15}{\left(x-3\right)\left(x^{2}+15\right)}$ have the same denominator, add them by adding their numerators.
Cancel out $x-3$ in both numerator and denominator.
$$\frac{x+3}{x^{2}+15}+\frac{1}{x-3}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $x^{2}+15$ and $x-3$ is $\left(x-3\right)\left(x^{2}+15\right)$. Multiply $\frac{x+3}{x^{2}+15}$ times $\frac{x-3}{x-3}$. Multiply $\frac{1}{x-3}$ times $\frac{x^{2}+15}{x^{2}+15}$.
Since $\frac{\left(x+3\right)\left(x-3\right)}{\left(x-3\right)\left(x^{2}+15\right)}$ and $\frac{x^{2}+15}{\left(x-3\right)\left(x^{2}+15\right)}$ have the same denominator, add them by adding their numerators.
