Solve 7/2x-3-5/3+2x=4/4x^2-9

$$\frac { 7 } { 2 x - 3 } - \frac { 5 } { 3 + 2 x } = \frac { 4 } { 4 x ^ { 2 } - 9 }$$

Solve for x

$$x=-8$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -\frac{3}{2},\frac{3}{2} since division by zero is not defined. Multiply both sides of the equation by \left(2x-3\right)\left(2x+3\right), the least common multiple of 2x-3,3+2x,4x^{2}-9.

$$\left(2x+3\right)\times 7-\left(2x-3\right)\times 5=4$$

Use the distributive property to multiply 2x+3 by 7.

$$14x+21-\left(2x-3\right)\times 5=4$$

Use the distributive property to multiply 2x-3 by 5.

$$14x+21-\left(10x-15\right)=4$$

To find the opposite of 10x-15, find the opposite of each term.

$$14x+21-10x+15=4$$

Combine 14x and -10x to get 4x.

$$4x+21+15=4$$

Add 21 and 15 to get 36.

$$4x+36=4$$

Subtract 36 from both sides.

$$4x=4-36$$

Subtract 36 from 4 to get -32.

$$4x=-32$$

Divide both sides by 4.

$$x=\frac{-32}{4}$$

Divide -32 by 4 to get -8.

$$x=-8$$