How do you find the asymptotes of an equation? What is the difference between the long division method and the

Question

How do you find the asymptotes of an equation? What is the difference between the long division method and the dominant rule method of finding asymptote?

the dominant rule method is something like (2x - 4) / (x^2 - 4) becomes 2x / x^2 when x tends to infinity but i don't know how it works?

Please try to show an example and use both ways to solve.

Answer 1

(2x - 4) / (x^2 - 4)
The asymtote of this equation is when

(x^2-4) = 0
Then the equation willbe undefined
So when x = 2 or -2

Answer 2

As X gets a starting to be form of great Y= (2x-4)/(X^2-4) gets closer and closer to Y=2x/x^2 this is merely Y=2/x as X gets increasing great Y=2/X gets as on the factor of 0 as you like and not in any respect will enhance one asymptote is hence the at once line X=0 As X procedures 0 Y gets greater with out certain and the closer to 0 X is the better is Y yet another asymptote is Y=0