Q:

Find $\lim _{x\to 1}\left(\frac{x^n-1}{x^m-1}\right)$

So I do know how to find the answer n/m, using l'hopital's rule, but how to find it without using that rule?
$\lim _{x\to 1}\left(\frac{x^n-1}{x^m-1}\right)=\frac{n}{m}$

A:

Hint:
$$\frac{x^n-1}{x^m-1}=\frac{x^{n-1}+x^{n-2}+\cdots+x+1}{x^{m-1}+x^{m-2}+\cdots+x+1}$$

