Do you really have to solve it by l'Hôpital rule ? You can write and .
The derivative of is
The derivative of is
So the ratio of the derivatives is
But that is just 9/4 times the reciprocal of the original fraction. If, by L'Hopital's rule, we must have the limit of the original fraction equal to the limit of that, we must have, calling the limit of the original fraction L, L= (9/4)(1/L). Can you solve that for L? Of course, technically, you should also prove that L'Hopital's rule actually works here- that the limit exists.