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## Homework Statement

Hi.

I have a problem finding the limit of two different problems - without use of l'Hôpital's rule. I only know how to do this with use of the l'Hôpital's rule, therefore I'm seeking help to solve this problem.

## Homework Equations

The problems are:

Determine the limits without using l'Hopital's rule:

lim (x-2)/((√(x^2-3)-x/2)

x->2

lim (2x-√(4x^2+3x))

x->∞

## The Attempt at a Solution

First thing first, the 1st problem.

I do not have any attempt at a solution yet, as I do not know how to go about to solve this problem. I should add that I have solved this problem graphically, and I know that the answer should be 2/3.

Should I attempt to simplify the expression (I'm a bit rusty on that, unfortunately), factorize the expression or how should I go about to solve this?

I'm a bit clueless here, but I have my books open, ready to make an effort into completing this problem.

Thanks for any input.