Let's make the problem a bit more interesting and assume that the limit is supposed to be as x goes to 1 rather than 0. You can then check using l'Hôpital's rule that the answer should be 2/3. But it has to be done using only algebraic manipulation, so l'Hôp is not allowed.
Let . Then as x goes to 1, u also goes to 1. So we want to find
Edit. Beaten by Danny.