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