How do I take the limit of this function? $$\lim_{x \to 2^+} \frac{3}{x-2} - \frac{6}{x^2-4}$$
I'm unable to simplify it, but when I put it into my calculator (i.ie i'll put 2.1, 2.0001, etc), I keep getting $15$.  When I try to simplify it, I get nowhere at all.  How can I make this answer be 15?

\begin{align}
& \frac{3}{x-2} - \frac{6}{x^2-4} = \frac3{x-2} - \frac{6}{(x-2)(x+2)} = \frac{3(x+2)}{(x-2)(x+2)} - \frac{6}{(x-2)(x+2)} \\[10pt]
= {} & \frac{3(x+2)-6}{(x-2)(x+2)} = \frac{3x}{(x-2)(x+2)} = \underbrace{\frac{1}{x-2}}_{\text{This }\to\,+\infty}\cdot\underbrace{\frac{3x}{x+2}}_{\text{This }\to\,3/2}.
\end{align}
