Questions relating to asymptotes

Hello, I've just started learning about asymptotes in school. The questions I have are:

1. To find the vertical asymptote, why do you have to equal the denominator to 0? And then find x.
2. "" "" "" horizontal "" , why do you have to divide the numerator and denominator by x?

Thank you very much for your help, if anyone knows about a website or book that actually explains why you have to do certain things to achieve a result, I would be grateful for a recommendation.

Vertical Asymptotes

horizontal and oblique asymptotes are covered on subsequent pages of the link ...