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