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

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

Solve for x

$$x=-5$$

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

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

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

$$2x^{2}-2x=\left(x-1\right)\left(2x+1\right)+2\times 3$$

Use the distributive property to multiply x-1 by 2x+1 and combine like terms.

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

Multiply 2 and 3 to get 6.

$$2x^{2}-2x=2x^{2}-x-1+6$$

Add -1 and 6 to get 5.

$$2x^{2}-2x=2x^{2}-x+5$$

Subtract 2x^{2} from both sides.

$$2x^{2}-2x-2x^{2}=-x+5$$

Combine 2x^{2} and -2x^{2} to get 0.

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

Add x to both sides.

$$-2x+x=5$$

Combine -2x and x to get -x.

$$-x=5$$

Multiply both sides by -1.

$$x=-5$$