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

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

Solve for x

$$x = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{1}{2},\frac{1}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x-1\right)\left(2x+1\right), the least common multiple of 2x+1,2x-1.

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

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

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

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

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

Use the distributive property to multiply 4x+2 by x.

$$4x-2-\left(4x^{2}+2x\right)=-\left(2x-1\right)\left(2x+1\right)$$

To find the opposite of 4x^{2}+2x, find the opposite of each term.

$$4x-2-4x^{2}-2x=-\left(2x-1\right)\left(2x+1\right)$$

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

$$2x-2-4x^{2}=-\left(2x-1\right)\left(2x+1\right)$$

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

$$2x-2-4x^{2}=\left(-2x+1\right)\left(2x+1\right)$$

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

$$2x-2-4x^{2}=-4x^{2}+1$$

Add 4x^{2} to both sides.

$$2x-2-4x^{2}+4x^{2}=1$$

Combine -4x^{2} and 4x^{2} to get 0.

$$2x-2=1$$

Add 2 to both sides.

$$2x=1+2$$

Add 1 and 2 to get 3.

$$2x=3$$

Divide both sides by 2.

$$x=\frac{3}{2}$$