Prove this version of L'Hopitals theorem

[marlen19861]

I need to prove this version of l'hospital's theorem.

If limf(x)=limg(x)=infinity (as x goes to infinity) then lim[f(x)/g(x)]=lim[f'(x)/g'(x)] (as x goes to infinity)

Any help please?

Thank you

 

[HallsofIvy]

Have you tried applying L'Hopital's rule to (1/g(x))/(1/f(x))?