Solve z/x-1=4/x^2-1

$$\frac { z } { x - 1 } = \frac { 4 } { x ^ { 2 } - 1 }$$

Solve for x

$$x=-1+\frac{4}{z}$$

$$z\neq 2\text{ and }z\neq 0$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -1,1 since division by zero is not defined. Multiply both sides of the equation by \left(x-1\right)\left(x+1\right), the least common multiple of x-1,x^{2}-1.

$$\left(x+1\right)z=4$$

Use the distributive property to multiply x+1 by z.

$$xz+z=4$$

Subtract z from both sides.

$$xz=4-z$$

The equation is in standard form.

$$zx=4-z$$

Divide both sides by z.

$$\frac{zx}{z}=\frac{4-z}{z}$$

Dividing by z undoes the multiplication by z.

$$x=\frac{4-z}{z}$$

Divide 4-z by z.

$$x=-1+\frac{4}{z}$$

Variable x cannot be equal to any of the values -1,1.

$$x=-1+\frac{4}{z}\text{, }x\neq -1\text{ and }x\neq 1$$

Solve for z

$$z=\frac{4}{x+1}$$

$$|x|\neq 1$$

Steps for Solving Linear Equation

Multiply both sides of the equation by \left(x-1\right)\left(x+1\right), the least common multiple of x-1,x^{2}-1.

$$\left(x+1\right)z=4$$

Divide both sides by x+1.

$$\frac{\left(x+1\right)z}{x+1}=\frac{4}{x+1}$$

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

$$z=\frac{4}{x+1}$$