Solve x+y+z=xyz

$$x + y + z = x y z$$

Solve for x

$$x=-\frac{y+z}{1-yz}$$

$$z=0\text{ or }y\neq \frac{1}{z}$$

Steps for Solving Linear Equation

Subtract xyz from both sides.

$$x+y+z-xyz=0$$

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

$$x+z-xyz=-y$$

Subtract z from both sides.

$$x-xyz=-y-z$$

Combine all terms containing x.

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

Divide both sides by 1-yz.

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

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

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

Divide -y-z by 1-yz.

$$x=-\frac{y+z}{1-yz}$$

Solve for y

$$y=-\frac{x+z}{1-xz}$$

$$z=0\text{ or }x\neq \frac{1}{z}$$

Steps for Solving Linear Equation

Subtract xyz from both sides.

$$x+y+z-xyz=0$$

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

$$y+z-xyz=-x$$

Subtract z from both sides.

$$y-xyz=-x-z$$

Combine all terms containing y.

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

Divide both sides by 1-xz.

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

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

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

Divide -x-z by 1-xz.

$$y=-\frac{x+z}{1-xz}$$