To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(a-2\right)\left(a-1\right)$ and $\left(a-3\right)\left(a-2\right)$ is $\left(a-3\right)\left(a-2\right)\left(a-1\right)$. Multiply $\frac{1}{\left(a-2\right)\left(a-1\right)}$ times $\frac{a-3}{a-3}$. Multiply $\frac{1}{\left(a-3\right)\left(a-2\right)}$ times $\frac{a-1}{a-1}$.
Since $\frac{a-3}{\left(a-3\right)\left(a-2\right)\left(a-1\right)}$ and $\frac{a-1}{\left(a-3\right)\left(a-2\right)\left(a-1\right)}$ 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 $\left(a-3\right)\left(a-1\right)$ and $\left(a-5\right)\left(a-3\right)$ is $\left(a-5\right)\left(a-3\right)\left(a-1\right)$. Multiply $\frac{2}{\left(a-3\right)\left(a-1\right)}$ times $\frac{a-5}{a-5}$. Multiply $\frac{2}{\left(a-5\right)\left(a-3\right)}$ times $\frac{a-1}{a-1}$.
Since $\frac{2\left(a-5\right)}{\left(a-5\right)\left(a-3\right)\left(a-1\right)}$ and $\frac{2\left(a-1\right)}{\left(a-5\right)\left(a-3\right)\left(a-1\right)}$ have the same denominator, add them by adding their numerators.
