Solve 20/x-20/x+2

$$\frac{ 20 }{ x } - \frac{ 20 }{ x+2 }$$

Evaluate

$$\frac{40}{x\left(x+2\right)}$$

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{20}{x} times \frac{x+2}{x+2}. Multiply \frac{20}{x+2} times \frac{x}{x}.

$$\frac{20\left(x+2\right)}{x\left(x+2\right)}-\frac{20x}{x\left(x+2\right)}$$

Since \frac{20\left(x+2\right)}{x\left(x+2\right)} and \frac{20x}{x\left(x+2\right)} have the same denominator, subtract them by subtracting their numerators.

$$\frac{20\left(x+2\right)-20x}{x\left(x+2\right)}$$

Do the multiplications in 20\left(x+2\right)-20x.

$$\frac{20x+40-20x}{x\left(x+2\right)}$$

Combine like terms in 20x+40-20x.

$$\frac{40}{x\left(x+2\right)}$$

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

$$\frac{40}{x^{2}+2x}$$

Factor

$$\frac{40}{x\left(x+2\right)}$$