Solve x+xy-y=0

$$x + x y - y = 0$$

Solve for x

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

$$y\neq -1$$

Steps for Solving Linear Equation

Add y to both sides. Anything plus zero gives itself.

$$x+xy=y$$

Combine all terms containing x.

$$\left(1+y\right)x=y$$

The equation is in standard form.

$$\left(y+1\right)x=y$$

Divide both sides by 1+y.

$$\frac{\left(y+1\right)x}{y+1}=\frac{y}{y+1}$$

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

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Subtract x from both sides. Anything subtracted from zero gives its negation.

$$xy-y=-x$$

Combine all terms containing y.

$$\left(x-1\right)y=-x$$

Divide both sides by x-1.

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

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

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