Limits in a 0/0 case

[RaptorsFan]

1. The problem statement, all variables and given/known data

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.


2. Relevant equations

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

3. 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

[Dick]

You better show us your attempt at doing some algebra and cancelling the x. Because it works for me.

[RaptorsFan]

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!

[DrMath]

Can try L'Hopital rule?

[trumpet-205]

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})