Solve x/x+2-x-2/x

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

Evaluate

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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

Expand

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

Short Solution Steps

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

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

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

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

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

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

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

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

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

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