Solve =y+y/x=1/x^2B

$$= y + \frac { y } { x } = \frac { 1 } { x ^ { 2 } } B$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{\sqrt{y^{2}+4By}}{2y}-\frac{1}{2}\text{, }&\left(arg(y)<\pi \text{ or }B\neq 0\right)\text{ and }y\neq 0\\x=\frac{\sqrt{y^{2}+4By}}{2y}-\frac{1}{2}\text{, }&\left(|\frac{arg(y^{2})}{2}-arg(y)|\geq \pi \text{ or }B\neq 0\right)\text{ and }y\neq 0\\x\neq 0\text{, }&y=0\text{ and }B=0\end{matrix}\right.$$

Solve for B

$$B=xy\left(x+1\right)$$

$$x\neq 0$$

Solve for x

$$\left\{\begin{matrix}x=-\frac{\sqrt{y^{2}+4By}}{2y}-\frac{1}{2}\text{, }&\left(B\neq 0\text{ and }y\leq -4B\text{ and }y<0\right)\text{ or }\left(B\neq 0\text{ and }y=-4B\right)\text{ or }\left(y>0\text{ and }y\geq -4B\right)\\x=\frac{\sqrt{y^{2}+4By}}{2y}-\frac{1}{2}\text{, }&\left(B\neq 0\text{ and }y\geq -4B\text{ and }y>0\right)\text{ or }\left(B\neq 0\text{ and }y=-4B\right)\text{ or }\left(y<0\text{ and }y\leq -4B\right)\\x\neq 0\text{, }&y=0\text{ and }B=0\end{matrix}\right.$$