Solve (2a/a-b+a-b/b)*b

$$( \frac { 2 a } { a - b } + \frac { a - b } { b } ) \cdot b$$

Evaluate

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

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}{b} times \frac{a-b}{a-b}.

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

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

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

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

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

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

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

Express \frac{b^{2}+a^{2}}{b\left(a-b\right)}b as a single fraction.

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

Cancel out b in both numerator and denominator.

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

Expand

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

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}{b} times \frac{a-b}{a-b}.

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

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

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

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

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

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

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

Express \frac{b^{2}+a^{2}}{b\left(a-b\right)}b as a single fraction.

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

Cancel out b in both numerator and denominator.

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