Answer
$\displaystyle \frac{2(x+3)}{3}$
Work Step by Step
Dividing with $\displaystyle \frac{P}{Q}$ equals multiplying with the reciprocal, $\displaystyle \frac{Q}{P}.$
$ \displaystyle \frac{4x^{2}+10}{x-3}\div\frac{6x^{2}+15}{x^{2}-9}=\frac{4x^{2}+10}{x-3}\cdot\frac{x^{2}-9}{6x^{2}+15}\qquad$... factor what you can
$\left[\begin{array}{l}
4x^{2}+10=2(x^{2}+5)\\
6x^{2}+15=3(x^{2}+5)\\
x^{2}-9=(x+3)(x-3)
\end{array}\right]$
$=\displaystyle \frac{2(x^{2}+5)}{(x-3)}\cdot\frac{(x+3)(x-3)}{3(x^{2}+5)}\qquad$... divide out the common factors
$=\displaystyle \frac{2(1)}{(1)}\cdot\frac{(x+3)(1)}{3(1)}{\ }$
= $\displaystyle \frac{2(x+3)}{3}$
