Solve z=x+1/xy

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

Solve for x

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

$$z\neq \frac{1}{y}\text{ and }y\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy.

$$zxy=x+1$$

Subtract x from both sides.

$$zxy-x=1$$

Combine all terms containing x.

$$\left(zy-1\right)x=1$$

The equation is in standard form.

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

Divide both sides by yz-1.

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

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

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

Variable x cannot be equal to 0.

$$x=\frac{1}{yz-1}\text{, }x\neq 0$$

Solve for y

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

Steps for Solving Linear Equation

Variable y cannot be equal to 0 since division by zero is not defined. Multiply both sides of the equation by xy.

$$zxy=x+1$$

Reorder the terms.

$$xyz=x+1$$

The equation is in standard form.

$$xzy=x+1$$

Divide both sides by xz.

$$\frac{xzy}{xz}=\frac{x+1}{xz}$$

Dividing by xz undoes the multiplication by xz.

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

Variable y cannot be equal to 0.

$$y=\frac{x+1}{xz}\text{, }y\neq 0$$