Solve 2/2x-6+8/2x+6=26/x^2-9

$$\frac { 2 } { 2 x - 6 } + \frac { 8 } { 2 x + 6 } = \frac { 26 } { x ^ { 2 } - 9 }$$

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 2\left(x-3\right)\left(x+3\right), the least common multiple of 2x-6,2x+6,x^{2}-9.

$$\left(x+3\right)\times 2+\left(x-3\right)\times 8=2\times 26$$

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

$$2x+6+\left(x-3\right)\times 8=2\times 26$$

Use the distributive property to multiply x-3 by 8.

$$2x+6+8x-24=2\times 26$$

Combine 2x and 8x to get 10x.

$$10x+6-24=2\times 26$$

Subtract 24 from 6 to get -18.

$$10x-18=2\times 26$$

Multiply 2 and 26 to get 52.

$$10x-18=52$$

Add 18 to both sides.

$$10x=52+18$$

Add 52 and 18 to get 70.

$$10x=70$$

Divide both sides by 10.

$$x=\frac{70}{10}$$

Divide 70 by 10 to get 7.

$$x=7$$