(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Find this crazy limit using algebraic manipulations. I've tried quite a bit of stuff and keep getting lost, can you recommend anything?

The answer is 2.

2. Relevant equations

[tex] \lim_{x \to - 1} \frac{108(x^2 \ + \ 2x)(x \ + \ 1)^3}{(x^3 \ + \ 1)^3(x \ - \ 1)} [/tex]

3. The attempt at a solution

[itex] \lim_{x \to - 1} \frac{108(x^2 \ + \ 2x)(x \ + \ 1)^2(x \ + \ 1)}{(x^3 \ + \ 1)^3(x \ - \ 1)} [/itex]

[itex] \lim_{x \to - 1} \frac{108(x^2 \ + \ 2x)(x ^2\ + \ 2x \ + \ 1)(x \ + \ 1)}{(x^3 \ + \ 1)^3(x \ - \ 1)} [/itex]

[itex] \lim_{x \to - 1} \frac{108(x^2 \ + \ 2x)(x ^3\ + \ 3x^2 \ + \ 3x \ + \ 1)}{(x^3 \ + \ 1)^3(x \ - \ 1)} [/itex]

If I were to keep going expanding I'll get x^10 on the bottom and x^5 on the top, it just gets so hairy & I can't find any commonality.

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# Homework Help: Not so Basic Limit!

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