Assuming that $3u + 12v\neq0$, simplify $\dfrac{12u^3 + 48u^2v}{3u+12v}$.
12u^3 + 48u^2v 12u^2 ( u + 4v) 12u^2
______________ = _________________ = ______ = 4u^2
3u + 12v 3 ( u + 4v) 3
