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