Solve a/a-b+a/b

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

Evaluate

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

Short Solution Steps

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

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

Since \frac{ab}{b\left(a-b\right)} and \frac{a\left(a-b\right)}{b\left(a-b\right)} have the same denominator, add them by adding their numerators.

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

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

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

Combine like terms in ab+a^{2}-ab.

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

Expand b\left(a-b\right).

$$\frac{a^{2}}{ab-b^{2}}$$

Factor

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