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

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

Evaluate

$$a+b$$

Short Solution Steps

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

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

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

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

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

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

Extract the negative sign in a-b.

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

Cancel out -a+b in both numerator and denominator.

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

Expand the expression.

$$a+b$$

Differentiate w.r.t. a

$$1$$