Solve x+y=x/y

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

Solve for x

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

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

Steps for Solving Linear Equation

Multiply both sides of the equation by y.

$$yx+yy=x$$

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

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

Subtract x from both sides.

$$yx+y^{2}-x=0$$

Subtract y^{2} from both sides. Anything subtracted from zero gives its negation.

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

Combine all terms containing x.

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

Divide both sides by y-1.

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

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

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

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

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

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