To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x-3\right)\left(x-2\right)$ and $\left(x-3\right)\left(-x+1\right)$ is $\left(x-3\right)\left(x-2\right)\left(-x+1\right)$. Multiply $\frac{1}{\left(x-3\right)\left(x-2\right)}$ times $\frac{-x+1}{-x+1}$. Multiply $\frac{2}{\left(x-3\right)\left(-x+1\right)}$ times $\frac{x-2}{x-2}$.
Since $\frac{-x+1}{\left(x-3\right)\left(x-2\right)\left(-x+1\right)}$ and $\frac{2\left(x-2\right)}{\left(x-3\right)\left(x-2\right)\left(-x+1\right)}$ 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 $\left(x-2\right)\left(-x+1\right)$ and $\left(x-2\right)\left(x-1\right)$ is $\left(x-2\right)\left(x-1\right)$. Multiply $\frac{1}{\left(x-2\right)\left(-x+1\right)}$ times $\frac{-1}{-1}$.
Since $\frac{-1}{\left(x-2\right)\left(x-1\right)}$ and $\frac{3}{\left(x-2\right)\left(x-1\right)}$ have the same denominator, subtract them by subtracting their numerators. Subtract $3$ from $-1$ to get $-4$.
