Question

$$X/A+B=X/B+A$$

Solve for A

$\left\{\begin{matrix}A=-\frac{X}{B}\text{, }&X\neq 0\text{ and }B\neq 0\\A=B\text{, }&B\neq 0\end{matrix}\right.$

Solve for B

$\left\{\begin{matrix}B=-\frac{X}{A}\text{, }&X\neq 0\text{ and }A\neq 0\\B=A\text{, }&A\neq 0\end{matrix}\right.$