Vertical/Horizontal asymptotes problem

Question

How do I find all vertical and horizontal asymptotes of the graph of the function?

f(x) x²-1/x²-2x-3

Answer 1

to find vertical asymptotes:

set denominator equal to zero (slope of vertical asymptote is infinity)

therefore,

x²-2x-3=0, then use factorization

(x-3)(x+1)=0

ans: vertical asymptotes at x=3 and x=-1

to find horizontal asymptotes:

notice the degree of numerator and the denominator are the same,

therefore,

horizontal asymptote equals leading coefficient of numerator over leading coefficient of denominator

H.A. at y=1