# Not so Basic Limit!

1. Apr 11, 2010

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?

2. Relevant equations

$$\lim_{x \to - 1} \frac{108(x^2 \ + \ 2x)(x \ + \ 1)^3}{(x^3 \ + \ 1)^3(x \ - \ 1)}$$

3. The attempt at a solution

$\lim_{x \to - 1} \frac{108(x^2 \ + \ 2x)(x \ + \ 1)^2(x \ + \ 1)}{(x^3 \ + \ 1)^3(x \ - \ 1)}$

$\lim_{x \to - 1} \frac{108(x^2 \ + \ 2x)(x ^2\ + \ 2x \ + \ 1)(x \ + \ 1)}{(x^3 \ + \ 1)^3(x \ - \ 1)}$

$\lim_{x \to - 1} \frac{108(x^2 \ + \ 2x)(x ^3\ + \ 3x^2 \ + \ 3x \ + \ 1)}{(x^3 \ + \ 1)^3(x \ - \ 1)}$

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.

2. Apr 11, 2010

### Gregg

Simplify it to

$$\frac{108 x (2+x)}{(x-1) \left(1-x+x^2\right)^3}$$

3. Apr 11, 2010

Ahh!!! I should have just realised to factor x³ + 1!!! So simple now thank you :)