Limit help, Calc I

[Ruffryder]

Hey guys, I pretty much know how to do these but I'm having troubles on getting the answer. The problem is :

Lim as x--->1 of (X^2 + X - 2)/(X^5 - 1)



If I plug 1 in the bottom is undefined, so i'm guessing I need to factor X^5 - 1. But I don't know how to factor this. Can anyone help me out? The answer is 3/5 but I can't get there. I would appreciate any help

 

[galactus]

Obviously, a zero of \(\displaystyle x^{5}-1\) is 1. So, divide it by x-1.

You get \(\displaystyle \L\\\frac{x^{5}-1}{x-1}=x^{4}+x^{3}+x^{2}+x+1\)

Factor \(\displaystyle \L\\x^{2}+x-2=(x-1)(x+2)\)

You get:

\(\displaystyle \L\\\frac{(x-1)(x+2)}{(x-1)(x^{4}+x^{3}+x^{2}+x+1)}\)

\(\displaystyle \L\\\lim_{x\to\1}\frac{x+2}{x^{4}+x^{3}+x^{2}+x+1}\)

 

[Ruffryder]

Ohh I didn't realize that I had to divide the X^5 -1 I knew it had some relationship with the X - 1 but couldn't figure out the rest. Thanks for the help, I really aprreciate itl.