# lim f/g = lim (f+o(1))/(g+o(1))

Let $\lim := \lim_{x \to a}$. Suppose $\lim f/g$ exists. Under what conditions can we say $\lim {f+o(1) \over g+o(1)}$ exists and is equal to $\lim f/g$? (Little o's are as $x\to a$.)