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?

$$\frac{3}{x-2} - \frac{6}{x^2-4} = \frac{3}{x-2} + \frac{3}{2}\frac{1}{x-2} -\frac{3}{2} \frac{1}{x+2} $$ $$= \frac{9}{2}\frac{1}{x-2} - \frac{3}{2}\frac{1}{x+2} $$
Since $$ \lim_{x\rightarrow 2^+} \frac{1}{x+2} = \frac{1}{4}$$
we have $$  \lim_{x\rightarrow 2^+} \bigg( \frac{9}{2}\frac{1}{x-2} - \frac{3}{2}\frac{1}{x+2} \bigg)=\infty$$
