Solve 1/x+4-2/x-4=4/x^2-16

$$\frac { 1 } { x + 4 } - \frac { 2 } { x - 4 } = \frac { 4 } { x ^ { 2 } - 16 }$$

Solve for x

$$x=-16$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply x+4 by 2.

$$x-4-\left(2x+8\right)=4$$

To find the opposite of 2x+8, find the opposite of each term.

$$x-4-2x-8=4$$

Combine x and -2x to get -x.

$$-x-4-8=4$$

Subtract 8 from -4 to get -12.

$$-x-12=4$$

Add 12 to both sides.

$$-x=4+12$$

Add 4 and 12 to get 16.

$$-x=16$$

Multiply both sides by -1.

$$x=-16$$