Solve xy+x+y=2

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

Solve for x

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

$$y\neq -1$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$xy+x=2-y$$

Combine all terms containing x.

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

Divide both sides by y+1.

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

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

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

Solve for y

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

$$x\neq -1$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$xy+y=2-x$$

Combine all terms containing y.

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

Divide both sides by x+1.

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

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

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