Solve 4/x-1-2/x+1=5/x^2-1

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

Solve for x

$$x=-\frac{1}{2}=-0.5$$

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.

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

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

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

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

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

To find the opposite of 2x-2, find the opposite of each term.

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

Combine 4x and -2x to get 2x.

$$2x+4+2=5$$

Add 4 and 2 to get 6.

$$2x+6=5$$

Subtract 6 from both sides.

$$2x=5-6$$

Subtract 6 from 5 to get -1.

$$2x=-1$$

Divide both sides by 2.

$$x=\frac{-1}{2}$$

Fraction \frac{-1}{2} can be rewritten as -\frac{1}{2} by extracting the negative sign.

$$x=-\frac{1}{2}$$