Suppose that g1(n) ∈ Θ(f1(n)) and g2(n) ∈ Θ(f2(n)), where g2 and f2 are eventually positive. Prove that g1(n)/g2(n) ∈ Θ(f1(n)/f2(n)) and show that this does not necessarily hold is if Θ is replaced with O.
I think I may have the first part figured out I just need some clarification, and I'm not sure exactly why this wouldnt hold for O.