Cancel out $a-3$ in both numerator and denominator.
$$\frac{a+3}{a-2}+\frac{a+3}{3a-6}$$
Factor $3a-6$.
$$\frac{a+3}{a-2}+\frac{a+3}{3\left(a-2\right)}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $a-2$ and $3\left(a-2\right)$ is $3\left(a-2\right)$. Multiply $\frac{a+3}{a-2}$ times $\frac{3}{3}$.
Since $\frac{3\left(a+3\right)}{3\left(a-2\right)}$ and $\frac{a+3}{3\left(a-2\right)}$ have the same denominator, add them by adding their numerators.
Cancel out $a-3$ in both numerator and denominator.
$$\frac{a+3}{a-2}+\frac{a+3}{3a-6}$$
Factor $3a-6$.
$$\frac{a+3}{a-2}+\frac{a+3}{3\left(a-2\right)}$$
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $a-2$ and $3\left(a-2\right)$ is $3\left(a-2\right)$. Multiply $\frac{a+3}{a-2}$ times $\frac{3}{3}$.
Since $\frac{3\left(a+3\right)}{3\left(a-2\right)}$ and $\frac{a+3}{3\left(a-2\right)}$ have the same denominator, add them by adding their numerators.
