Answer
V.A. $x=7$, H.A. $y=3$
Work Step by Step
Step 1. Simplify the expression $R(x)=\frac{3(x^2-4)}{(x+2)(x-7)}=\frac{3(x+2)(x-2)}{(x+2)(x-7)}=\frac{3(x-2)}{x-7},\ x\ne-2$
Step 2. We can find the vertical asymptote as $x=7$
Step 3. The horizontal asymptote is the ratio of the leading coefficients $y=\frac{3}{1}=3$
