Solve 12/x^2+2x-2/x

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

Evaluate

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

Short Solution Steps

Factor x^{2}+2x.

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

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

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

Since \frac{12}{x\left(x+2\right)} and \frac{2\left(x+2\right)}{x\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 12-2\left(x+2\right).

$$\frac{12-2x-4}{x\left(x+2\right)}$$

Combine like terms in 12-2x-4.

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

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

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

Factor

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