Solve a/x-a/x+b

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

Evaluate

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

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{a}{x} times \frac{x+b}{x+b}. Multiply \frac{a}{x+b} times \frac{x}{x}.

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

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

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

Do the multiplications in a\left(x+b\right)-ax.

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

Combine like terms in ax+ab-ax.

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

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

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

Factor

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