Given that $\displaystyle h$ is a continuous func. on the compact set $\displaystyle K$ such that $\displaystyle h(x) \neq 0$ on $\displaystyle K$, and also given that $\displaystyle (g_n)$ is a sequence of functions such that they converge uniformly to $\displaystyle g$ on $\displaystyle K$, prove $\displaystyle \left(\frac{g_n}{h}\right)$ converges uniformly to $\displaystyle \frac{g}{h}$ on $\displaystyle K$.

Not sure. Apparently its a very hard proof.