Chapter 6 - Section 6.1 - Rational Functions and Multiplying and Dividing Rational Expressions - Exercise Set - Page 346: 61

$r^2-rs+s^2$

Factoring the expressions and then cancelling the common factor/s between the numerator and the denominator, then the given expression, $ \dfrac{r^3+s^3}{r+s} $, simplifies to \begin{array}{l}\require{cancel} \dfrac{(r+s)(r^2-rs+s^2)}{r+s} \\\\= \dfrac{(\cancel{r+s})(r^2-rs+s^2)}{\cancel{r+s}} \\\\= r^2-rs+s^2 .\end{array}