Solve xyz=x+y+z

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

Solve for x

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

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

Steps for Solving Linear Equation

Subtract x from both sides.

$$xyz-x=y+z$$

Combine all terms containing x.

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

Divide both sides by yz-1.

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

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

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

Solve for y

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

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

Steps for Solving Linear Equation

Subtract y from both sides.

$$xyz-y=x+z$$

Combine all terms containing y.

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

Divide both sides by xz-1.

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

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

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