Solve (4)1/x+1+2/x-1=4/x^2-1quad(5)

$$( 4 ) \frac { 1 } { x + 1 } + \frac { 2 } { x - 1 } = \frac { 4 } { x ^ { 2 } - 1 } \quad ( 5 )$$

Solve for x

$$x = \frac{11}{3} = 3\frac{2}{3} \approx 3.666666667$$

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.

$$4\left(x-1\right)\times 1+\left(x+1\right)\times 2=4\times 5$$

Multiply 4 and 1 to get 4.

$$4\left(x-1\right)+\left(x+1\right)\times 2=4\times 5$$

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

$$4x-4+\left(x+1\right)\times 2=4\times 5$$

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

$$4x-4+2x+2=4\times 5$$

Combine 4x and 2x to get 6x.

$$6x-4+2=4\times 5$$

Add -4 and 2 to get -2.

$$6x-2=4\times 5$$

Multiply 4 and 5 to get 20.

$$6x-2=20$$

Add 2 to both sides.

$$6x=20+2$$

Add 20 and 2 to get 22.

$$6x=22$$

Divide both sides by 6.

$$x=\frac{22}{6}$$

Reduce the fraction \frac{22}{6} to lowest terms by extracting and canceling out 2.

$$x=\frac{11}{3}$$