Solve 12/3x-2-8/3x+2=2-33x/4-9x^2

$$\frac { 12 } { 3 x - 2 } - \frac { 8 } { 3 x + 2 } = \frac { 2 - 33 x } { 4 - 9 x ^ { 2 } }$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

$$\left(3x+2\right)\times 12-\left(3x-2\right)\times 8=-\left(2-33x\right)$$

Use the distributive property to multiply 3x+2 by 12.

$$36x+24-\left(3x-2\right)\times 8=-\left(2-33x\right)$$

Use the distributive property to multiply 3x-2 by 8.

$$36x+24-\left(24x-16\right)=-\left(2-33x\right)$$

To find the opposite of 24x-16, find the opposite of each term.

$$36x+24-24x+16=-\left(2-33x\right)$$

Combine 36x and -24x to get 12x.

$$12x+24+16=-\left(2-33x\right)$$

Add 24 and 16 to get 40.

$$12x+40=-\left(2-33x\right)$$

To find the opposite of 2-33x, find the opposite of each term.

$$12x+40=-2+33x$$

Subtract 33x from both sides.

$$12x+40-33x=-2$$

Combine 12x and -33x to get -21x.

$$-21x+40=-2$$

Subtract 40 from both sides.

$$-21x=-2-40$$

Subtract 40 from -2 to get -42.

$$-21x=-42$$

Divide both sides by -21.

$$x=\frac{-42}{-21}$$

Divide -42 by -21 to get 2.

$$x=2$$