I'm having a bit of trouble with epsilon-delta proofs of limits. I have to prove the existence of the limit $\lim_{x \to -3} \frac{x^2 + x - 6}{x^2 - 9} = \frac{5}{6}.$
I want to try to relate $\delta$ and $\varepsilon$ through $0 < |x + 3| < \delta$ and $\left| \frac{x^2+x-6}{x^2-9} - 5/6 \right| < \varepsilon,$ but that's where I'm stuck. Everything I've done up to this point has come out very cleanly when I try to relate $\delta$ and $\varepsilon$ (e.g. $\delta = \varepsilon/3$), but I don't see a way to do that this time.
Thanks.