Solve 2a/a+b-a/b

$$\frac { 2 a } { a + b } - \frac { a } { b }$$

Evaluate

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

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{2a}{a+b} times \frac{b}{b}. Multiply \frac{a}{b} times \frac{a+b}{a+b}.

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

Since \frac{2ab}{b\left(a+b\right)} and \frac{a\left(a+b\right)}{b\left(a+b\right)} have the same denominator, subtract them by subtracting their numerators.

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

Do the multiplications in 2ab-a\left(a+b\right).

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

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

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

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

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

Factor

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