Solve xy-y+2x+2=0

$$xy-y+2x+2=0$$

Solve for x

$$x=-\frac{2-y}{y+2}$$

$$y\neq -2$$

Steps for Solving Linear Equation

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

$$xy+2x+2=y$$

Subtract 2 from both sides.

$$xy+2x=y-2$$

Combine all terms containing x.

$$\left(y+2\right)x=y-2$$

Divide both sides by y+2.

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

Dividing by y+2 undoes the multiplication by y+2.

$$x=\frac{y-2}{y+2}$$

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Subtract 2x from both sides. Anything subtracted from zero gives its negation.

$$xy-y+2=-2x$$

Subtract 2 from both sides.

$$xy-y=-2x-2$$

Combine all terms containing y.

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

Divide both sides by x-1.

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

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

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

Divide -2x-2 by x-1.

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