Solve 2/x-x/x+2

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

Factor

$$-\frac{\left(x-\left(1-\sqrt{5}\right)\right)\left(x-\left(\sqrt{5}+1\right)\right)}{x\left(x+2\right)}$$