Simplify (a^2)/(a-b)+(b^2)/(b-a)

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

Step 1

Simplify terms.

Factor $- 1$ out of $b$ .

$\frac{a^{2}}{a - b} + \frac{b^{2}}{- 1 (- b) - a}$

Factor $- 1$ out of $- a$ .

$\frac{a^{2}}{a - b} + \frac{b^{2}}{- 1 (- b) - (a)}$

Factor $- 1$ out of $- 1 (- b) - (a)$ .

$\frac{a^{2}}{a - b} + \frac{b^{2}}{- 1 (- b + a)}$

Simplify the expression.

Move a negative from the denominator of $\frac{b^{2}}{- 1 (- b + a)}$ to the numerator.

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

Reorder terms.

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

Combine the numerators over the common denominator.

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

Step 2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

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

Step 3

Cancel the common factor of $a - b$ .

Cancel the common factor.

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

Divide $a + b$ by $1$ .

$a + b$