Question

$$\frac{ x-a }{ b } + \frac{ x-b }{ a } + \frac{ x-3a-3b }{ a+b } =0$$

Solve for a

$\left\{\begin{matrix}a=x-b\text{, }&x\neq b\text{ and }x\neq 0\text{ and }b\neq 0\\a=\frac{\left(-\sqrt{5}-3\right)b}{2}\text{; }a=\frac{\left(\sqrt{5}-3\right)b}{2}\text{, }&b\neq 0\end{matrix}\right.$

Solve for b

$\left\{\begin{matrix}b=x-a\text{, }&x\neq 0\text{ and }x\neq a\text{ and }a\neq 0\\b=\frac{\left(-\sqrt{5}-3\right)a}{2}\text{; }b=\frac{\left(\sqrt{5}-3\right)a}{2}\text{, }&a\neq 0\end{matrix}\right.$