Solve 6/x^2-2x-8/x^2-4

$$\frac { 6 } { x ^ { 2 } - 2 x } - \frac { 8 } { x ^ { 2 } - 4 }$$

Evaluate

$$\frac{2\left(6-x\right)}{x\left(x^{2}-4\right)}$$

Short Solution Steps

Factor x^{2}-2x. Factor x^{2}-4.

$$\frac{6}{x\left(x-2\right)}-\frac{8}{\left(x-2\right)\left(x+2\right)}$$

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x\left(x-2\right) and \left(x-2\right)\left(x+2\right) is x\left(x-2\right)\left(x+2\right). Multiply \frac{6}{x\left(x-2\right)} times \frac{x+2}{x+2}. Multiply \frac{8}{\left(x-2\right)\left(x+2\right)} times \frac{x}{x}.

$$\frac{6\left(x+2\right)}{x\left(x-2\right)\left(x+2\right)}-\frac{8x}{x\left(x-2\right)\left(x+2\right)}$$

Since \frac{6\left(x+2\right)}{x\left(x-2\right)\left(x+2\right)} and \frac{8x}{x\left(x-2\right)\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{6\left(x+2\right)-8x}{x\left(x-2\right)\left(x+2\right)}$$

Do the multiplications in 6\left(x+2\right)-8x.

$$\frac{6x+12-8x}{x\left(x-2\right)\left(x+2\right)}$$

Combine like terms in 6x+12-8x.

$$\frac{-2x+12}{x\left(x-2\right)\left(x+2\right)}$$

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

$$\frac{-2x+12}{x^{3}-4x}$$

Factor

$$\frac{2\left(6-x\right)}{x\left(x^{2}-4\right)}$$