Solve x/+y/x+z/e=1

$$\frac{ x }{ } + \frac{ y }{ x } + \frac{ z }{ e } = 1$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\frac{-\sqrt{e^{2}-2ez+z^{2}-4e^{2}y}-z+e}{2e}\text{, }&\left(arg(e-z)\geq \pi \text{ and }z\neq e\right)\text{ or }y\neq 0\\x=\frac{\sqrt{e^{2}-2ez+z^{2}-4e^{2}y}-z+e}{2e}\text{, }&\left(z\neq e\text{ and }arg(e-z)<\pi \right)\text{ or }y\neq 0\end{matrix}\right.$$

Solve for x

$$\left\{\begin{matrix}x=\frac{-\sqrt{e^{2}-2ez+z^{2}-4e^{2}y}-z+e}{2e}\text{, }&\left(e-z<0\text{ or }y\neq 0\right)\text{ and }y\leq \frac{\left(e-z\right)^{2}}{4e^{2}}\text{ and }\left(y\neq 0\text{ or }z>e\right)\\x=\frac{\sqrt{e^{2}-2ez+z^{2}-4e^{2}y}-z+e}{2e}\text{, }&\left(-\left(e-z\right)<0\text{ or }y\neq 0\right)\text{ and }y\leq \frac{\left(e-z\right)^{2}}{4e^{2}}\text{ and }\left(y\neq 0\text{ or }z<e\right)\end{matrix}\right.$$

Solve for y

$$y=-\frac{x\left(ex+z-e\right)}{e}$$

$$x\neq 0$$