Limits in 0/0 Calculus I Problem

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Homework Statement



I'm in the early stages of Calculus I.. just doing the basics you learn in the Calc prep course.
This one problem is really getting me confused.


Homework Equations



Lim -> 0 in the function 1/x(1/(x+2)^2 -1/4)

The Attempt at a Solution



I've tried foiling and cancelling, it hasn't worked.
I've tried a^2 - b^2 formula to cancel, that hasn't worked either
Tried using a conjugate without a root and that doesn't work
Would this be a case where 'The Squeeze' method would be necessary? Or is there a better way.. Thanks in advance
 
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You better show us your attempt at doing some algebra and cancelling the x. Because it works for me.
 
After about 10 attempts later and numerous sign errors and not simplifying stuff enough i finally got an answer of -1/4.. Thanks anyway guys!
 
Can try L'Hopital rule?
 
Lim -> 0 in the function 1/x(1/(x+2)^2 -1/4)

Do you mean this?

\lim_{x\to 0}\frac{1}{x} (\frac{1}{(x+2)^{2}} - \frac{1}{4})
 
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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