Solve xz/z-1=1/z-1+2

$$\frac { x z } { z - 1 } = \frac { 1 } { z - 1 } + 2$$

Solve for x

$$x=2-\frac{1}{z}$$

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

Steps for Solving Linear Equation

Multiply both sides of the equation by z-1.

$$xz=1+\left(z-1\right)\times 2$$

Use the distributive property to multiply z-1 by 2.

$$xz=1+2z-2$$

Subtract 2 from 1 to get -1.

$$xz=-1+2z$$

The equation is in standard form.

$$zx=2z-1$$

Divide both sides by z.

$$\frac{zx}{z}=\frac{2z-1}{z}$$

Dividing by z undoes the multiplication by z.

$$x=\frac{2z-1}{z}$$

Divide -1+2z by z.

$$x=2-\frac{1}{z}$$

Solve for z

$$z=-\frac{1}{x-2}$$

$$x\neq 1\text{ and }x\neq 2$$

Steps for Solving Linear Equation

Variable z cannot be equal to 1 since division by zero is not defined. Multiply both sides of the equation by z-1.

$$xz=1+\left(z-1\right)\times 2$$

Use the distributive property to multiply z-1 by 2.

$$xz=1+2z-2$$

Subtract 2 from 1 to get -1.

$$xz=-1+2z$$

Subtract 2z from both sides.

$$xz-2z=-1$$

Combine all terms containing z.

$$\left(x-2\right)z=-1$$

Divide both sides by x-2.

$$\frac{\left(x-2\right)z}{x-2}=-\frac{1}{x-2}$$

Dividing by x-2 undoes the multiplication by x-2.

$$z=-\frac{1}{x-2}$$

Variable z cannot be equal to 1.

$$z=-\frac{1}{x-2}\text{, }z\neq 1$$