Solve $\dfrac{x - a}{x - b} + \dfrac{x - b}{x - a} = \dfrac{a}{b} + \dfrac{b}{a}$:

Writing $t=\frac{x-a}{x-b}$, the equation becomes $t+\frac{1}{t}=\frac{a}{b}+\frac{b}{a}$, whose solutions correspond to $\frac{x-a}{x-b}=\frac{a}{b}$ or $\frac{b}{a}$. Solving these gives $x=0$ or $x=a+b$.