Solve x/y+z=y

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

Solve for x

$$x=-y\left(z-y\right)$$

$$y\neq 0$$

Solution Steps

Multiply both sides of the equation by y.

$$x+yz=yy$$

Multiply y and y to get y^{2}.

$$x+yz=y^{2}$$

Subtract yz from both sides.

$$x=y^{2}-yz$$

Solve for y

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