Answer
domain $(-\infty,-\frac{3}{2})U(-\frac{3}{2},2)U(2,\infty)$
Horizontal asymptote $y=3$
Vertical asymptote $x=-\frac{3}{2}$
Work Step by Step
Step 1. Factor the function to get $R(x)=\frac{(6x+1)(x-2)}{(2x+3)(x-2)}=\frac{6x+1}{2x+3}, (x\ne2)$
Step 2. We can determine the domain as $(-\infty,-\frac{3}{2})U(-\frac{3}{2},2)U(2,\infty)$
Step 3. We can identify a horizontal asymptote $y=3$ and a vertical asymptote $x=-\frac{3}{2}$
