The question is as follows:

Use l'Hopital's rule to evaluate

lim [(a^x - b^x) / (e^ax - e^bx)] when x approaches 0. (Notice: e here stands for exponential symbol).

The answer given by the textbook is (lna - lnb) / (a - b). However, I have problem of getting to this answer. In particular, I don't know how to obtain (a - b) in the denominator.

Please show me the steps of getting to answer. thank you in advance