HMMT November 2008 U29

Let $p(x)$ be the polynomial of degree 4 with roots $1,2,3,4$ and leading coefficient 1 . Let $q(x)$ be the polynomial of degree 4 with roots $1, \frac{1}{2}, \frac{1}{3}$, and $\frac{1}{4}$ and leading coefficient 1 . Find $\lim _{x \rightarrow 1} \frac{p(x)}{q(x)}$.