Solve 9/2x+1-8x/2x-1=-4

$$\frac { 9 } { 2 x + 1 } - \frac { 8 x } { 2 x - 1 } = - 4$$

Solve for x

$$x = \frac{13}{10} = 1\frac{3}{10} = 1.3$$

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.

$$\left(2x-1\right)\times 9-\left(2x+1\right)\times 8x=-4\left(2x-1\right)\left(2x+1\right)$$

Use the distributive property to multiply 2x-1 by 9.

$$18x-9-\left(2x+1\right)\times 8x=-4\left(2x-1\right)\left(2x+1\right)$$

Use the distributive property to multiply 2x+1 by 8.

$$18x-9-\left(16x+8\right)x=-4\left(2x-1\right)\left(2x+1\right)$$

Use the distributive property to multiply 16x+8 by x.

$$18x-9-\left(16x^{2}+8x\right)=-4\left(2x-1\right)\left(2x+1\right)$$

To find the opposite of 16x^{2}+8x, find the opposite of each term.

$$18x-9-16x^{2}-8x=-4\left(2x-1\right)\left(2x+1\right)$$

Combine 18x and -8x to get 10x.

$$10x-9-16x^{2}=-4\left(2x-1\right)\left(2x+1\right)$$

Use the distributive property to multiply -4 by 2x-1.

$$10x-9-16x^{2}=\left(-8x+4\right)\left(2x+1\right)$$

Use the distributive property to multiply -8x+4 by 2x+1 and combine like terms.

$$10x-9-16x^{2}=-16x^{2}+4$$

Add 16x^{2} to both sides.

$$10x-9-16x^{2}+16x^{2}=4$$

Combine -16x^{2} and 16x^{2} to get 0.

$$10x-9=4$$

Add 9 to both sides.

$$10x=4+9$$

Add 4 and 9 to get 13.

$$10x=13$$

Divide both sides by 10.

$$x=\frac{13}{10}$$