You're a little mixed up about how to find horizontal asymptotes.
You don't set the numerator equal to 0 to find the horizontal
asymptote.  Apparently that's what you were thinking.  You need to
review how to find horizontal asymptotes.



You found vertical asymptotes OK:

Set denominator = 0


Factor:




  That's the equation of one vertical asymptote


  That's the equation of the other asymptote

Here they are:

 

Since the largest exponent in the top is smaller than the exponent in the
bottom, the x-axis, whose equation is y=0, is the horizontal asymptote:

 

It's hard to tell what the graph does on the right. It crosses the
x-axis at 1, it goes up just a tiny bit (less than one tenth),
then it goes back down and approaches the x-axis on the right.

Edwin