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

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

Evaluate

$$a+b$$

Short Solution Steps

To add or subtract expressions, expand them to make their denominators the same. Least common multiple of b-a and a-b is a-b. Multiply \frac{b^{2}}{b-a} times \frac{-1}{-1}.

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

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

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

Factor the expressions that are not already factored in \frac{-b^{2}+a^{2}}{a-b}.

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

Extract the negative sign in b-a.

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

Cancel out a-b in both numerator and denominator.

$$-\left(-a-b\right)$$

Expand the expression.

$$a+b$$

Differentiate w.r.t. b

$$1$$