Solve 3/2x+1=2/2x-1-x+1/4x^2-1

$$\frac { 3 } { 2 x + 1 } = \frac { 2 } { 2 x - 1 } - \frac { x + 1 } { 4 x ^ { 2 } - 1 }$$

Solve for x

$$x = \frac{4}{3} = 1\frac{1}{3} \approx 1.333333333$$

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-1,4x^{2}-1.

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

Use the distributive property to multiply 2x-1 by 3.

$$6x-3=\left(2x+1\right)\times 2-\left(x+1\right)$$

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

$$6x-3=4x+2-\left(x+1\right)$$

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

$$6x-3=4x+2-x-1$$

Combine 4x and -x to get 3x.

$$6x-3=3x+2-1$$

Subtract 1 from 2 to get 1.

$$6x-3=3x+1$$

Subtract 3x from both sides.

$$6x-3-3x=1$$

Combine 6x and -3x to get 3x.

$$3x-3=1$$

Add 3 to both sides.

$$3x=1+3$$

Add 1 and 3 to get 4.

$$3x=4$$

Divide both sides by 3.

$$x=\frac{4}{3}$$