In general, the procedure for asymptotes is the following:
set the denominator equal to zero and solve
the zeroes (if any) are the vertical asymptotes
everything else is the domain
compare the degrees of the numerator and the denominator
if the degrees are the same, then you have a horizontal asymptote at y = (numerator's leading coefficient) / (denominator's leading coefficient)
if the denominator's degree is greater (by any margin), then you have a horizontal asymptote at y = 0 (the x-axis)
if the numerator's degree is greater (by a margin of 1), then you have a slant asymptote which you will find by doing long division
This applet will illustrate the division of two functions, D(x) and N(x).
