Question

find all the asymptotes of the function f(x) =x-3/x^2-1

Answer 1

vertical asymptotes were denominator is zero
solve
\[x^2-1=0\] get
\[x=1, x=-1\] and those are your vertical asymptotes

Answer 2

since the degree of the numerator is less than the degree of the denominator, you have a horizontal asymptote at
\[y=0\]