Solve xy+yz-xz=1

$$x y + y z - x z = 1$$

Solve for x

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

Steps for Solving Linear Equation

Subtract yz from both sides.

$$xy-xz=1-yz$$

Combine all terms containing x.

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

Divide both sides by y-z.

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

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

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

Solve for y

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

Steps for Solving Linear Equation

Add xz to both sides.

$$xy+yz=1+xz$$

Combine all terms containing y.

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

The equation is in standard form.

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

Divide both sides by x+z.

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

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

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