# Find limit of the following function

## 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

## 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???

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

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!

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

Could you perhaps tell me what this different method is?

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.

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