Solve a+b+2b^2/a-b

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

Evaluate

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

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Multiply a+b times \frac{a-b}{a-b}.

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

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

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

Do the multiplications in \left(a+b\right)\left(a-b\right)+2b^{2}.

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

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

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

Differentiate w.r.t. b

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