Answer
$3x^{2}+3xh+h^{2}$
Work Step by Step
In the numerator, expand
$(x+h)^{3}=\left(\begin{array}{l}
3\\
0
\end{array}\right)x^{3}h^{0}+\left(\begin{array}{l}
3\\
1
\end{array}\right)x^{2}h^{1}+\left(\begin{array}{l}
3\\
2
\end{array}\right)x^{1}h^{2}+\left(\begin{array}{l}
3\\
3
\end{array}\right)h^{5}$
$\displaystyle \frac{(x+h)^{3}-x^{3}}{h}=\frac{x^{3}+3x^{2}h+3xh^{2}+h^{3}-x^{3}}{h}$
$=\displaystyle \frac{3x^{2}h+3xh^{2}+h^{3}}{h}$
..factor out h in the numerator...
$=\displaystyle \frac{h(3x^{2}+3xh+h^{2})}{h}$
...reduce ...
$=3x^{2}+3xh+h^{2}$
