Solve 2/x+2+5/x-2=6/x^2-4

$$\frac { 2 } { x + 2 } + \frac { 5 } { x - 2 } = \frac { 6 } { x ^ { 2 } - 4 }$$

Solve for x

$$x=0$$

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.

$$\left(x-2\right)\times 2+\left(x+2\right)\times 5=6$$

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

$$2x-4+\left(x+2\right)\times 5=6$$

Use the distributive property to multiply x+2 by 5.

$$2x-4+5x+10=6$$

Combine 2x and 5x to get 7x.

$$7x-4+10=6$$

Add -4 and 10 to get 6.

$$7x+6=6$$

Subtract 6 from both sides.

$$7x=6-6$$

Subtract 6 from 6 to get 0.

$$7x=0$$

Product of two numbers is equal to 0 if at least one of them is 0. Since 7 is not equal to 0, x must be equal to 0.

$$x=0$$