Solve 2/4x^2-9+1/2x-3=3/2x+3

$$\frac { 2 } { 4 x ^ { 2 } - 9 } + \frac { 1 } { 2 x - 3 } = \frac { 3 } { 2 x + 3 }$$

Solve for x

$$x = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

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 4x^{2}-9,2x-3,2x+3.

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

Add 2 and 3 to get 5.

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

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

$$5+2x=6x-9$$

Subtract 6x from both sides.

$$5+2x-6x=-9$$

Combine 2x and -6x to get -4x.

$$5-4x=-9$$

Subtract 5 from both sides.

$$-4x=-9-5$$

Subtract 5 from -9 to get -14.

$$-4x=-14$$

Divide both sides by -4.

$$x=\frac{-14}{-4}$$

Reduce the fraction \frac{-14}{-4} to lowest terms by extracting and canceling out -2.

$$x=\frac{7}{2}$$