To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(x-5\right)\left(x-4\right)$ and $\left(x-6\right)\left(x-5\right)$ is $\left(x-6\right)\left(x-5\right)\left(x-4\right)$. Multiply $\frac{1}{\left(x-5\right)\left(x-4\right)}$ times $\frac{x-6}{x-6}$. Multiply $\frac{1}{\left(x-6\right)\left(x-5\right)}$ times $\frac{x-4}{x-4}$.
Since $\frac{x-6}{\left(x-6\right)\left(x-5\right)\left(x-4\right)}$ and $\frac{x-4}{\left(x-6\right)\left(x-5\right)\left(x-4\right)}$ have the same denominator, add them by adding their numerators.
