Solve 2x/x^2-4-2

$$\frac { 2 x } { x ^ { 2 } - 4 } - 2$$

Evaluate

$$\frac{2\left(4+x-x^{2}\right)}{x^{2}-4}$$

Short Solution Steps

Factor x^{2}-4.

$$\frac{2x}{\left(x-2\right)\left(x+2\right)}-2$$

To add or subtract expressions, expand them to make their denominators the same. Multiply 2 times \frac{\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}.

$$\frac{2x}{\left(x-2\right)\left(x+2\right)}-\frac{2\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$$

Since \frac{2x}{\left(x-2\right)\left(x+2\right)} and \frac{2\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{2x-2\left(x-2\right)\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}$$

Do the multiplications in 2x-2\left(x-2\right)\left(x+2\right).

$$\frac{2x-2x^{2}-4x+4x+8}{\left(x-2\right)\left(x+2\right)}$$

Combine like terms in 2x-2x^{2}-4x+4x+8.

$$\frac{2x-2x^{2}+8}{\left(x-2\right)\left(x+2\right)}$$

Expand \left(x-2\right)\left(x+2\right).

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

Factor

$$-\frac{2\left(x-\frac{1-\sqrt{17}}{2}\right)\left(x-\frac{\sqrt{17}+1}{2}\right)}{x^{2}-4}$$