Solve 4/x-1+2/x+1=35/x^2-1

$$\frac{ 4 }{ x-1 } + \frac{ 2 }{ x+1 } = \frac{ 35 }{ { x }^{ 2 } -1 }$$

Solve for x

$$x = \frac{11}{2} = 5\frac{1}{2} = 5.5$$

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.

$$\left(x+1\right)\times 4+\left(x-1\right)\times 2=35$$

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

$$4x+4+\left(x-1\right)\times 2=35$$

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

$$4x+4+2x-2=35$$

Combine 4x and 2x to get 6x.

$$6x+4-2=35$$

Subtract 2 from 4 to get 2.

$$6x+2=35$$

Subtract 2 from both sides.

$$6x=35-2$$

Subtract 2 from 35 to get 33.

$$6x=33$$

Divide both sides by 6.

$$x=\frac{33}{6}$$

Reduce the fraction \frac{33}{6} to lowest terms by extracting and canceling out 3.

$$x=\frac{11}{2}$$