Solve xyz+x+y+z+xy+xz+yz=1989

$$xyz+x+y+z+xy+xz+yz=1989$$

Solve for x

$$x=-\frac{yz+y+z-1989}{yz+y+z+1}$$

$$z\neq -1\text{ and }y\neq -1$$

Steps for Solving Linear Equation

Subtract y from both sides.

$$xyz+x+z+xy+xz+yz=1989-y$$

Subtract z from both sides.

$$xyz+x+xy+xz+yz=1989-y-z$$

Subtract yz from both sides.

$$xyz+x+xy+xz=1989-y-z-yz$$

Combine all terms containing x.

$$\left(yz+1+y+z\right)x=1989-y-z-yz$$

The equation is in standard form.

$$\left(yz+y+z+1\right)x=1989-z-y-yz$$

Divide both sides by yz+1+y+z.

$$\frac{\left(yz+y+z+1\right)x}{yz+y+z+1}=\frac{1989-z-y-yz}{yz+y+z+1}$$

Dividing by yz+1+y+z undoes the multiplication by yz+1+y+z.

$$x=\frac{1989-z-y-yz}{yz+y+z+1}$$

Solve for y

$$y=-\frac{xz+x+z-1989}{xz+x+z+1}$$

$$z\neq -1\text{ and }x\neq -1$$

Steps for Solving Linear Equation

Subtract x from both sides.

$$xyz+y+z+xy+xz+yz=1989-x$$

Subtract z from both sides.

$$xyz+y+xy+xz+yz=1989-x-z$$

Subtract xz from both sides.

$$xyz+y+xy+yz=1989-x-z-xz$$

Combine all terms containing y.

$$\left(xz+1+x+z\right)y=1989-x-z-xz$$

The equation is in standard form.

$$\left(xz+x+z+1\right)y=1989-z-x-xz$$

Divide both sides by xz+1+x+z.

$$\frac{\left(xz+x+z+1\right)y}{xz+x+z+1}=\frac{1989-z-x-xz}{xz+x+z+1}$$

Dividing by xz+1+x+z undoes the multiplication by xz+1+x+z.

$$y=\frac{1989-z-x-xz}{xz+x+z+1}$$