$$\quad \frac { a } { x - b } + \frac { b } { x - a } = 2$$
$\left\{\begin{matrix}a=x-b\text{, }&b\neq 0\text{ and }x\neq b\\a=2x-b\text{, }&x\neq b\end{matrix}\right.$
$\left\{\begin{matrix}b=2x-a\text{, }&a\neq x\\b=x-a\text{, }&a\neq 0\text{ and }a\neq x\end{matrix}\right.$