1. The problem statement, all variables and given/known data 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. 2. Relevant 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->∞ 3. 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.