[Edwin McCravy and AnlytcPhil are the same person!]



We multiply the numerator out:



Place the numerator in descending order of powers of x:



Since the degree of the numerator is 2 and the degree
of the denominator is also 2, the equation of the
horizontal asymptote is 







The green line is the horizontal asymptote.  It's hard to tell but on
the left the graph actually crosses its horizontal asymptote at x= -3.5,
goes a tiny bit below it and then approaches it from below.  On the right
the graph only approaches the horizontal asymptote from above.

Edwin