To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $a+3$ and $a-3$ is $\left(a-3\right)\left(a+3\right)$. Multiply $\frac{2a}{a+3}$ times $\frac{a-3}{a-3}$. Multiply $\frac{3a}{a-3}$ times $\frac{a+3}{a+3}$.
Since $\frac{2a\left(a-3\right)}{\left(a-3\right)\left(a+3\right)}$ and $\frac{3a\left(a+3\right)}{\left(a-3\right)\left(a+3\right)}$ have the same denominator, add them by adding their numerators.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(a-3\right)\left(a+3\right)$ and $9+a^{2}$ is $\left(a-3\right)\left(a+3\right)\left(a^{2}+9\right)$. Multiply $\frac{5a^{2}+3a}{\left(a-3\right)\left(a+3\right)}$ times $\frac{a^{2}+9}{a^{2}+9}$. Multiply $\frac{2a}{9+a^{2}}$ times $\frac{\left(a-3\right)\left(a+3\right)}{\left(a-3\right)\left(a+3\right)}$.
Since $\frac{\left(5a^{2}+3a\right)\left(a^{2}+9\right)}{\left(a-3\right)\left(a+3\right)\left(a^{2}+9\right)}$ and $\frac{2a\left(a-3\right)\left(a+3\right)}{\left(a-3\right)\left(a+3\right)\left(a^{2}+9\right)}$ have the same denominator, add them by adding their numerators.
