I've been working on these two problems for some time and cannot get either of them to work. ( I don't know how to use Math HTML so bear with me )

Find the Limit

Problem 1: lim [ (x/x-1) - (1/lnx) ]

x->1

Problem 2: lim [ sqrt(x^2 + x) - x ]

x->inf

I've been working for quite a while. The solution to both problems is 1/2