Question 912127
Your second equation with the {{{1/6}}} factor is a polynomial and has no asymptotes.  


Your third equation has horizontal asymptote of {{{-2/3}}} toward the left and {{{-2/3}}} toward the right; which you can tell by seeing degree of numerator and denominator are the same and examining each extreme case.  A vertical asymptote is for 5-3x=0 meaning {{{x=5/3}}} is the vertical asymptote.


First equation is undefined for x=3 so this is the vertical asymptote.  Degree of numerator is one more than degree of denominator, so ... you can find the slant asymptote; perform the division and consider what happens to the remainder for x extreme in either direction.  The quotient tells you the slant asymptote.