firstly, how do you get from a function like: x-1 + (1/x-3) to the original function before long division?

and secondly i know how you find the asymptotes of a funtion like:

(x^2 + 3)/(x+2)

but how do you get them if it is:

(x+2)/(x^2+3)

??

cheers and thanks very appreciated!