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

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

Solve for x

$$x=-14$$

Steps for Solving Linear Equation

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

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

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

$$4x-8-\left(x+2\right)\times 3=2x$$

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

$$4x-8-\left(3x+6\right)=2x$$

To find the opposite of 3x+6, find the opposite of each term.

$$4x-8-3x-6=2x$$

Combine 4x and -3x to get x.

$$x-8-6=2x$$

Subtract 6 from -8 to get -14.

$$x-14=2x$$

Subtract 2x from both sides.

$$x-14-2x=0$$

Combine x and -2x to get -x.

$$-x-14=0$$

Add 14 to both sides. Anything plus zero gives itself.

$$-x=14$$

Multiply both sides by -1.

$$x=-14$$