Answer
$x=-\frac{3}{2}$ is Vertical Asymptote
$y=3$ is the Horizontal Asymptote
Work Step by Step
$R(x)=\frac{6x^2-11x-2}{2x^2-x-6}$
$n=2, m=2$.
$n$ being the leading coefficient of the numerator and $m$ being the leading coefficient of the denominator.
The leading coefficient of the numerator and that of denominator is equal.
$n=m,$ Thus, $y=\frac{6}{2}=3$ is the Horizontal Asymptote
Factorizing the denominator,
$2x^2-x-6,$
$=2x^2-4x+3x-6,$
$=2x(x-2)+3(x-2),$
$=(2x+3)(x-2),$
Therefore, $R(x)=\frac{6x^2-11x-2}{(2x+3)(x-2)}=\frac{(x-2)(6x+1)}{(2x+3)(x-2)}=\frac{6x+1}{2x+3}$.
$x=-\frac{3}{2}$ is Vertical Asymptote
