Calculus: Can you help me find a limit

Alright, the problem reads like so:

(x-1) /
[√(x+3) - 2]

And I have to find the limit as it approaches 1 mathematically. (This would be so much easier with a graph...)

I multiplied by the conjugate, √(x+3) + 2, but that just left me with x + 3 - 4 on the bottom, which of course is 4 - 4 when 1 is used for x, so that did zero good.

What do I do now? I'm so lost. A shove in the right direction would be fully appreciated.

"..just left me with x + 3 - 4 on the bottom, which of course is 4 - 4.." How about leaving it as x-1 and canceling it with the x-1 in the numerator?

Glad to be of help.

And take a break. Math and not functioning well is not a good combination.

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The form a/0 in limits (a is not 0) is either infinity or negative infinity depending on direction.

Are you approaching 1 from above or below?

If above then it'll be +infinity because sqrt(x+3) will be ever so slightly greater than 2 as you approach the limit.

If below then -infinity for much the same reason

The easiest way to solve this is to use L'Hopitals rule:
lim(x-->1) (x-1)/(√(x+3) - 2) = lim(x-->1) 1/[(1/2)(1/(√(x+3)) = lim(x-->1)2√(x+3) = 4.
Answer: 4.