To add or subtract expressions, expand them to make their denominators the same. Least common multiple of $a-b$ and $b-a$ is $-a+b$. Multiply $\frac{a}{a-b}$ times $\frac{-1}{-1}$.
$$\frac{-a}{-a+b}+\frac{b}{-a+b}$$
Since $\frac{-a}{-a+b}$ and $\frac{b}{-a+b}$ have the same denominator, add them by adding their numerators.
$$\frac{-a+b}{-a+b}$$
Cancel out $-a+b$ in both numerator and denominator.
