Solve xy-y=x+x

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

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

Combine x and x to get 2x.

$$xy-y=2x$$

Subtract 2x from both sides.

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

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

$$xy-2x=y$$

Combine all terms containing x.

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

Divide both sides by y-2.

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

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

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Combine x and x to get 2x.

$$xy-y=2x$$

Combine all terms containing y.

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

Divide both sides by x-1.

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

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

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