There's an error in your version of the function. Â Compare yours to the original post.
Consider what happens to this function as x becomes increasingly large:
the denominator grows quickly and without bound. Â The numerator stays the same. Â In such a situation, the function goes to zero as x increases. Â Thus, y = 0 is the horiz. asympt. Â The denom. is never zero, so there are no vert. asymp.