Solve 1/x+1-1/x

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of x+1 and x is x\left(x+1\right). Multiply \frac{1}{x+1} times \frac{x}{x}. Multiply \frac{1}{x} times \frac{x+1}{x+1}.

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

Since \frac{x}{x\left(x+1\right)} and \frac{x+1}{x\left(x+1\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in x-\left(x+1\right).

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

Combine like terms in x-x-1.

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

Expand x\left(x+1\right).

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

Differentiate w.r.t. x

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