Solve xy+yz+xz=xyz

$$xy+yz+xz=xyz$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=-\frac{yz}{z+y-yz}\text{, }&z=1\text{ or }y\neq -\frac{z}{1-z}\\x\in \mathrm{C}\text{, }&y=0\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract xyz from both sides.

$$xy+yz+xz-xyz=0$$

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

$$xy+xz-xyz=-yz$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y+z-yz.

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

Dividing by y+z-yz undoes the multiplication by y+z-yz.

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

Solve for y (complex solution)

$$\left\{\begin{matrix}y=-\frac{xz}{z+x-xz}\text{, }&z=1\text{ or }x\neq -\frac{z}{1-z}\\y\in \mathrm{C}\text{, }&x=0\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract xyz from both sides.

$$xy+yz+xz-xyz=0$$

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

$$xy+yz-xyz=-xz$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by x+z-xz.

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

Dividing by x+z-xz undoes the multiplication by x+z-xz.

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

Solve for x

$$\left\{\begin{matrix}x=-\frac{yz}{z+y-yz}\text{, }&z=1\text{ or }y\neq -\frac{z}{1-z}\\x\in \mathrm{R}\text{, }&y=0\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract xyz from both sides.

$$xy+yz+xz-xyz=0$$

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

$$xy+xz-xyz=-yz$$

Combine all terms containing x.

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

The equation is in standard form.

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

Divide both sides by y+z-yz.

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

Dividing by y+z-yz undoes the multiplication by y+z-yz.

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

Solve for y

$$\left\{\begin{matrix}y=-\frac{xz}{z+x-xz}\text{, }&z=1\text{ or }x\neq -\frac{z}{1-z}\\y\in \mathrm{R}\text{, }&x=0\text{ and }z=0\end{matrix}\right.$$

Steps for Solving Linear Equation

Subtract xyz from both sides.

$$xy+yz+xz-xyz=0$$

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

$$xy+yz-xyz=-xz$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by x+z-xz.

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

Dividing by x+z-xz undoes the multiplication by x+z-xz.

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