Solve 1/x^2+x-12-2/x^2-16=0

$$\frac { 1 } { x ^ { 2 } + x - 12 } - \frac { 2 } { x ^ { 2 } - 16 } = 0$$

Solve for x

$$x=2$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values -4,3,4 since division by zero is not defined. Multiply both sides of the equation by \left(x-4\right)\left(x-3\right)\left(x+4\right), the least common multiple of x^{2}+x-12,x^{2}-16.

$$x-4-\left(x-3\right)\times 2=0$$

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

$$x-4-\left(2x-6\right)=0$$

To find the opposite of 2x-6, find the opposite of each term.

$$x-4-2x+6=0$$

Combine x and -2x to get -x.

$$-x-4+6=0$$

Add -4 and 6 to get 2.

$$-x+2=0$$

Subtract 2 from both sides. Anything subtracted from zero gives its negation.

$$-x=-2$$

Multiply both sides by -1.

$$x=2$$