Exploring the Limits of f(x): P(x)/Q(x)

[EV33]

Homework Statement

P(x)=a0*x^(p)+a1*x^(p-1)+a2*x^(p-2)...
Q(x)=b0*x^(q)+b1*x^(q-1)+b2*x^(q-2)...

f(x)=lim (n$$\rightarrow$$$$\infty$$)P(n)/Q(n)

prove what f(x) is equal to for when p<q,q<p,p=q

Find the different values of f(x)

Homework Equations

The only information that I know I can use is the definition of a limit, the squeeze principle,, 1/n converges as n goes to infinity, the limit of a^n where a is a fixed number, and that you can multiply, add, and divide limits.

The Attempt at a Solution

Let
P(n)/Q(n)=(a0*n^(p)+a1*n^(p-1)+a2*n^(p-2)...)/(b0*n^(q)+b1*n^(q-1)+b2*n^(q-2)...)
I'll just start off by asking my first question. It is not legal to divide the top by n^p and the bottom by n^q correct? I would assume its not ok to do because the ratio between the two is not 1.

 

[EV33]

If my wording isn't clear please let me know and I can reword what I said.