Solve 1/x-1/x+b

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

Evaluate

$$\frac{b}{x\left(x+b\right)}$$

Short Solution Steps

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

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

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

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

Combine like terms in x+b-x.

$$\frac{b}{x\left(x+b\right)}$$

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

$$\frac{b}{x^{2}+bx}$$

Differentiate w.r.t. x

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