Solve 1/x-1/x-2

$$\frac{ 1 }{ x } - \frac{ 1 }{ x-2 }$$

Evaluate

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

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{1}{x} times \frac{x-2}{x-2}. Multiply \frac{1}{x-2} times \frac{x}{x}.

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

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

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

Combine like terms in x-2-x.

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

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

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

Differentiate w.r.t. x

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