To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(a-3\right)\left(a-4\right)$ and $\left(a-4\right)\left(a-5\right)$ is $\left(a-5\right)\left(a-4\right)\left(a-3\right)$. Multiply $\frac{1}{\left(a-3\right)\left(a-4\right)}$ times $\frac{a-5}{a-5}$. Multiply $\frac{1}{\left(a-4\right)\left(a-5\right)}$ times $\frac{a-3}{a-3}$.
Since $\frac{a-5}{\left(a-5\right)\left(a-4\right)\left(a-3\right)}$ and $\frac{a-3}{\left(a-5\right)\left(a-4\right)\left(a-3\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{2}{\left(a-5\right)\left(a-3\right)}$ and $\frac{1}{\left(a-5\right)\left(a-3\right)}$ have the same denominator, add them by adding their numerators. Add $2$ and $1$ to get $3$.
To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $\left(a-3\right)\left(a-4\right)$ and $\left(a-4\right)\left(a-5\right)$ is $\left(a-5\right)\left(a-4\right)\left(a-3\right)$. Multiply $\frac{1}{\left(a-3\right)\left(a-4\right)}$ times $\frac{a-5}{a-5}$. Multiply $\frac{1}{\left(a-4\right)\left(a-5\right)}$ times $\frac{a-3}{a-3}$.
Since $\frac{a-5}{\left(a-5\right)\left(a-4\right)\left(a-3\right)}$ and $\frac{a-3}{\left(a-5\right)\left(a-4\right)\left(a-3\right)}$ have the same denominator, add them by adding their numerators.
Since $\frac{2}{\left(a-5\right)\left(a-3\right)}$ and $\frac{1}{\left(a-5\right)\left(a-3\right)}$ have the same denominator, add them by adding their numerators. Add $2$ and $1$ to get $3$.
