1) If the degree of the denominator is greater than the degree of the numerator, the HA is y=0
2) If the degrees of the numerator & denominator are the same, the HA is the ratio of the leading coefficients
3) If the degree of the numerator is larger than the denominator there is not a HA
In terms of finding which it is, you can factor it all out and see what the degrees of each will be.
Hope that helps!