- #1
sponsoredwalk
- 533
- 5
Homework Statement
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.
Homework Equations
[tex] \lim_{x \to - 1} \frac{108(x^2 \ + \ 2x)(x \ + \ 1)^3}{(x^3 \ + \ 1)^3(x \ - \ 1)} [/tex]
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.