Solve left(x+1right)left(y+2right)=2xy

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

Solve for x

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

$$y\neq 2$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by y+2.

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

Subtract 2xy from both sides.

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

Combine xy and -2xy to get -xy.

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

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

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

Subtract 2 from both sides.

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

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by -y+2.

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

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

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

Divide -y-2 by -y+2.

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

Solve for y

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

$$x\neq 1$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by y+2.

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

Subtract 2xy from both sides.

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

Combine xy and -2xy to get -xy.

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

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.

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

The equation is in standard form.

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

Divide both sides by -x+1.

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

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

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

Divide -2x-2 by -x+1.

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