Solve 16/x-3-20/x+3=12x-4/x^2-9

$$\frac { 16 } { x - 3 } - \frac { 20 } { x + 3 } = \frac { 12 x - 4 } { x ^ { 2 } - 9 }$$

Solve for x

$$x=7$$

Steps for Solving Linear Equation

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

$$\left(x+3\right)\times 16-\left(x-3\right)\times 20=12x-4$$

Use the distributive property to multiply x+3 by 16.

$$16x+48-\left(x-3\right)\times 20=12x-4$$

Use the distributive property to multiply x-3 by 20.

$$16x+48-\left(20x-60\right)=12x-4$$

To find the opposite of 20x-60, find the opposite of each term.

$$16x+48-20x+60=12x-4$$

Combine 16x and -20x to get -4x.

$$-4x+48+60=12x-4$$

Add 48 and 60 to get 108.

$$-4x+108=12x-4$$

Subtract 12x from both sides.

$$-4x+108-12x=-4$$

Combine -4x and -12x to get -16x.

$$-16x+108=-4$$

Subtract 108 from both sides.

$$-16x=-4-108$$

Subtract 108 from -4 to get -112.

$$-16x=-112$$

Divide both sides by -16.

$$x=\frac{-112}{-16}$$

Divide -112 by -16 to get 7.

$$x=7$$