Find limit of the following function

[Zipzap]

Homework Statement

lim (x->2) ((|x-3|-1)/(x^2 - 4) )

http://www.wolframalpha.com/input/?i=lim+%28x-%3E2%29+%28%28|x-3|-1%29%2F%28x^2+-+4%29+%29
^In case the above equation was unclear

Homework Equations

The Attempt at a Solution

I'm not really sure as to how I'm supposed to approach this problem. I know that I have to factor the denominator and do something to the numerator so that something cancels out. I also tried approaching from both sides, but that didn't do anything at all. Can anybody tell me what to do?

 

[dreit]

Technically this could be an indeterminate form, which means that you could try using L'Hopitals rule to go about finding this limit

 

[Zipzap]

See, I know that I have to do that. The problem is, our class hasn't been taught that rule yet, so I had the notion that there was another way by which I could find the limit. Of course, I'll probably have to email my professor to see if that's the case. Thanks for the clarification!

 

[dreit]

Ya, this could be solved by a different method, but I personally find L'Hopitals rule significantly easier. Hope I was of a little assistance at least

 

[Zipzap]

Could you perhaps tell me what this different method is?

 

[╔(σ_σ)╝]

Get rid of the absolute value sign :-)

When x is around 2; x-3 <0 so |x-3|=-(x-3)

Factor the denominator after getting rid the absolute value sign and you will arrive at your answer.

 

[Zipzap]

Yeah, that totally makes sense. I was about to put the sign for (x-3) as negative, but for some reason I didn't solve it completely, which would've given me my final answer. Thanks a lot! =D