Solve x/y=x-y

$$\frac{ x }{ y } =x-y$$

Solve for x

$$x=-\frac{y^{2}}{1-y}$$

$$y\neq 1\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$x=yx-yy$$

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

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

Subtract yx from both sides.

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

Combine all terms containing x.

$$\left(1-y\right)x=-y^{2}$$

Divide both sides by -y+1.

$$\frac{\left(1-y\right)x}{1-y}=-\frac{y^{2}}{1-y}$$

Dividing by -y+1 undoes the multiplication by -y+1.

$$x=-\frac{y^{2}}{1-y}$$

Solve for y (complex solution)

$$y=\frac{\sqrt{x\left(x-4\right)}+x}{2}$$

$$y=\frac{-\sqrt{x\left(x-4\right)}+x}{2}\text{, }x\neq 0$$

Solve for y

$$y=\frac{\sqrt{x\left(x-4\right)}+x}{2}$$

$$y=\frac{-\sqrt{x\left(x-4\right)}+x}{2}\text{, }x\geq 4\text{ or }x<0$$