What is $(a^3+b^3)\div(a^2-ab+b^2)$ when $a=5$ and $b=4$?
I recognize that the numerator of the fraction is a sum of cubes, and there is a formula for factoring that: $a^3+b^3=(a+b)(a^2-ab+b^2)$. So I can rewrite the fraction as $\frac{(a+b)(a^2-ab+b^2)}{a^2-ab+b^2}$. Now I see that the denominator is the same as one of the factors in the numerator, so I can cancel them out and simplify the fraction to $a+b$. Finally, I just need to plug in the values of $a$ and $b$ that are given: $a=5$ and $b=4$, so $a+b=5+4=9$. 