Question 1068030
{{{f(x)=(2x-3x^2)/(2x^2-x-3)}}}


{{{f(x)=(2x-3x^2)/(2x^2-x-3) =(-3x^2+2x)/(2x^2-x-3)}}}


The leading terms of numerator and denominator are of equal degree, and these leading terms become increasingly important for extreme x values to the left or to the right.  The ratio of their coefficients become the horizontal asymptote.

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{{{highlight(y=-3/2)}}}      Horizontal Asymptote
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