Solve 4/x-1+2/x+1=3/x^2-1

$$\frac { 4 } { x - 1 } + \frac { 2 } { x + 1 } = \frac { 3 } { x ^ { 2 } - 1 }$$

Solve for x

$$x=\frac{1}{6}\approx 0.166666667$$

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.

$$\left(x+1\right)\times 4+\left(x-1\right)\times 2=3$$

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

$$4x+4+\left(x-1\right)\times 2=3$$

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

$$4x+4+2x-2=3$$

Combine 4x and 2x to get 6x.

$$6x+4-2=3$$

Subtract 2 from 4 to get 2.

$$6x+2=3$$

Subtract 2 from both sides.

$$6x=3-2$$

Subtract 2 from 3 to get 1.

$$6x=1$$

Divide both sides by 6.

$$x=\frac{1}{6}$$