Solve 4/x-1+2/x+1=32/x^2-1

$$\frac { 4 } { x - 1 } + \frac { 2 } { x + 1 } = \frac { 32 } { x ^ { 2 } - 1 }$$

Solve for x

$$x=5$$

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+1,x^{2}-1.

$$\left(x+1\right)\times 4+\left(x-1\right)\times 2=32$$

Use the distributive property to multiply x+1 by 4.

$$4x+4+\left(x-1\right)\times 2=32$$

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

$$4x+4+2x-2=32$$

Combine 4x and 2x to get 6x.

$$6x+4-2=32$$

Subtract 2 from 4 to get 2.

$$6x+2=32$$

Subtract 2 from both sides.

$$6x=32-2$$

Subtract 2 from 32 to get 30.

$$6x=30$$

Divide both sides by 6.

$$x=\frac{30}{6}$$

Divide 30 by 6 to get 5.

$$x=5$$