Solve 1/x-1+5/x+1-x/x^2-1=3/2x-2

$$\frac { 1 } { x - 1 } + \frac { 5 } { x + 1 } - \frac { x } { x ^ { 2 } - 1 } = \frac { 3 } { 2 x - 2 }$$

Solve for x

$$x = \frac{11}{7} = 1\frac{4}{7} \approx 1.571428571$$

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

$$2x+2+\left(2x-2\right)\times 5-2x=\left(x+1\right)\times 3$$

Use the distributive property to multiply 2x-2 by 5.

$$2x+2+10x-10-2x=\left(x+1\right)\times 3$$

Combine 2x and 10x to get 12x.

$$12x+2-10-2x=\left(x+1\right)\times 3$$

Subtract 10 from 2 to get -8.

$$12x-8-2x=\left(x+1\right)\times 3$$

Combine 12x and -2x to get 10x.

$$10x-8=\left(x+1\right)\times 3$$

Use the distributive property to multiply x+1 by 3.

$$10x-8=3x+3$$

Subtract 3x from both sides.

$$10x-8-3x=3$$

Combine 10x and -3x to get 7x.

$$7x-8=3$$

Add 8 to both sides.

$$7x=3+8$$

Add 3 and 8 to get 11.

$$7x=11$$

Divide both sides by 7.

$$x=\frac{11}{7}$$