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The denominator cannot equal zero so the vertical asymptotes when one of the zeros of occurs.
4*-3=-12, the 2 factors of -12 whose sum is -4 is -6 and +2.
x=3/2 and x=-1/2 the vertical asymptotes.
If the largest exponent in the numerator is smaller than the largest in the denominator the the horizontal asymptote is zero. Graphs frequently cross horizontal asymptotes as in this case.