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Consider the limit

$$\lim_{x\to2} \frac{1}{x-2} - \frac{4}{x^2-4}$$

I just need help with the implementation of this limit. Is the best way of solving it to multiply out the fraction?

So,$$ \frac{x^2-4-4(x-2)}{(x-2)(x^2-4)}$$

And if that's the case... where do I go from there?

I'm sorry if this is extremely elementary!

Aaron Maroja
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Gil
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    $$\lim_{x\rightarrow 2}\left[\frac{1}{x-2} - \frac{4}{x^2-4}\right]$$ is the limit you want? – Chinny84 Dec 10 '14 at 15:33
  • Yes, sorry I didn't have it formatted well. – Gil Dec 10 '14 at 15:36
  • No worries. Just hover over my comment and click view latex (I believe) and then see how i format and then edit your post. Also check out the mathjax page on meta here. Good luck – Chinny84 Dec 10 '14 at 15:42

2 Answers2

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$$\begin{align}\lim_{x\to2} \frac{1}{x-2} - \frac{4}{x^2-4}&= \lim_{x\to2} \frac{x+2 -4}{x^2-4}\\&= \lim_{x\to2} \frac{x-2}{(x-2)(x+2)}\end{align} $$

I'm sure you can take it from here.

Aaron Maroja
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Since you get the indeterminant form $\infty -\infty$, when you try to plug in $2@, subtract the two fractions and simplify.

Tim Raczkowski
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