I'm trying to find a way to prove this:
EDIT: without using LHopital theorem. $\lim_{x\rightarrow 1}\frac{x^{1/m}-1}{x^{1/n}-1}=\frac{n}{m}.$ Honestly, I didn't come with any good idea.
We know that $\lim_{x\rightarrow 1}x^{1/m}$ is $1$.
I'd love your help with this.
Thank you.