To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(a-3\right)\left(a-2\right)$ and $\left(a-1\right)\left(3-a\right)$ is $\left(a-3\right)\left(a-2\right)\left(a-1\right)$. Multiply $\frac{1}{\left(a-3\right)\left(a-2\right)}$ times $\frac{a-1}{a-1}$. Multiply $\frac{2}{\left(a-1\right)\left(3-a\right)}$ times $\frac{-\left(a-2\right)}{-\left(a-2\right)}$.
Since $\frac{a-1}{\left(a-3\right)\left(a-2\right)\left(a-1\right)}$ and $\frac{2\left(-1\right)\left(a-2\right)}{\left(a-3\right)\left(a-2\right)\left(a-1\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{-1}{\left(a-2\right)\left(a-1\right)}$ and $\frac{1}{\left(a-2\right)\left(a-1\right)}$ have the same denominator, add them by adding their numerators. Add $-1$ and $1$ to get $0$.
