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