Calculating the limit at infinity of a rational function

[EnterTheArena]

Hello all, I'm having a trouble with calculating the limit at infinity of a rational function. The main source of my confusion is that the degrees of the terms are given as a variable rather than a straight number, and I'm not sure how to approach these.

For example, one of the problems is:

Calculate the limit of x-> infinity for
x^y
_______
(9x-z)^y

Where both y and z are constants and y > 1. I understand how to do this when y and z are given as straight numbers, but am unsure how to proceed in this form. Any direction would be appreciated.

 

[pka]

For example, one of the problems is:
Calculate the limit of x-> infinity for
x^y
_______
(9x-z)^y
Where both y and z are constants and y > 1.

It is a matter of simple algebra.
\(\displaystyle \dfrac{x^y}{(9x-z)^y}=\dfrac{1}{\left(9-\dfrac{z}{x}\right)^y}\).

 

[EnterTheArena]

Thanks so much. Do you have any resources you could direct me to that I could use to see more examples like this? I tried searching online, but am unable to find example with multiple variables like this.