Solve 2/2x+1+x/4x^2-1=7/2x-1

$$\frac{ 2 }{ 2x+1 } + \frac{ x }{ 4 { x }^{ 2 } -1 } = \frac{ 7 }{ 2x-1 }$$

Solve for x

$$x=-1$$

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

$$\left(2x-1\right)\times 2+x=\left(2x+1\right)\times 7$$

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

$$4x-2+x=\left(2x+1\right)\times 7$$

Combine 4x and x to get 5x.

$$5x-2=\left(2x+1\right)\times 7$$

Use the distributive property to multiply 2x+1 by 7.

$$5x-2=14x+7$$

Subtract 14x from both sides.

$$5x-2-14x=7$$

Combine 5x and -14x to get -9x.

$$-9x-2=7$$

Add 2 to both sides.

$$-9x=7+2$$

Add 7 and 2 to get 9.

$$-9x=9$$

Divide both sides by -9.

$$x=\frac{9}{-9}$$

Divide 9 by -9 to get -1.

$$x=-1$$