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

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

Evaluate

$$\frac{4\left(x+1\right)}{x\left(x+2\right)}$$

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{x+2}{x} times \frac{x+2}{x+2}. Multiply \frac{x}{x+2} times \frac{x}{x}.

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

Since \frac{\left(x+2\right)\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.

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

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

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

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

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

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

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

Expand

$$\frac{4\left(x+1\right)}{x\left(x+2\right)}$$

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{x+2}{x} times \frac{x+2}{x+2}. Multiply \frac{x}{x+2} times \frac{x}{x}.

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

Since \frac{\left(x+2\right)\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.

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

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

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

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

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

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

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