Solve 2x/x^2-4=8/x+2-1/x-2

$$\frac { 2 x } { x ^ { 2 } - 4 } = \frac { 8 } { x + 2 } - \frac { 1 } { x - 2 }$$

Solve for x

$$x = \frac{18}{5} = 3\frac{3}{5} = 3.6$$

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}-4,x+2,x-2.

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

Use the distributive property to multiply x-2 by 8.

$$2x=8x-16-\left(x+2\right)$$

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

$$2x=8x-16-x-2$$

Combine 8x and -x to get 7x.

$$2x=7x-16-2$$

Subtract 2 from -16 to get -18.

$$2x=7x-18$$

Subtract 7x from both sides.

$$2x-7x=-18$$

Combine 2x and -7x to get -5x.

$$-5x=-18$$

Divide both sides by -5.

$$x=\frac{-18}{-5}$$

Fraction \frac{-18}{-5} can be simplified to \frac{18}{5} by removing the negative sign from both the numerator and the denominator.

$$x=\frac{18}{5}$$