Solve x+1/2-2x^2-2x-1/x^2-1+6/x+1+1/2-2x=0

$$\frac{ x+1 }{ 2-2 { x }^{ 2 } } - \frac{ 2x-1 }{ { x }^{ 2 } -1 } + \frac{ 6 }{ x+1 } + \frac{ 1 }{ 2-2x } = 0$$

Solve for x

$$x=2$$

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 2-2x^{2},x^{2}-1,x+1,2-2x.

$$-\left(x+1\right)-2\left(2x-1\right)+\left(2x-2\right)\times 6-\left(1+x\right)=0$$

To find the opposite of x+1, find the opposite of each term.

$$-x-1-2\left(2x-1\right)+\left(2x-2\right)\times 6-\left(1+x\right)=0$$

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

$$-x-1-4x+2+\left(2x-2\right)\times 6-\left(1+x\right)=0$$

Combine -x and -4x to get -5x.

$$-5x-1+2+\left(2x-2\right)\times 6-\left(1+x\right)=0$$

Add -1 and 2 to get 1.

$$-5x+1+\left(2x-2\right)\times 6-\left(1+x\right)=0$$

Use the distributive property to multiply 2x-2 by 6.

$$-5x+1+12x-12-\left(1+x\right)=0$$

Combine -5x and 12x to get 7x.

$$7x+1-12-\left(1+x\right)=0$$

Subtract 12 from 1 to get -11.

$$7x-11-\left(1+x\right)=0$$

To find the opposite of 1+x, find the opposite of each term.

$$7x-11-1-x=0$$

Subtract 1 from -11 to get -12.

$$7x-12-x=0$$

Combine 7x and -x to get 6x.

$$6x-12=0$$

Add 12 to both sides. Anything plus zero gives itself.

$$6x=12$$

Divide both sides by 6.

$$x=\frac{12}{6}$$

Divide 12 by 6 to get 2.

$$x=2$$