More parenthesis might help.
The limit of [(x-1)/(x^2(x+2))] as x-> 0:
The denominator goes to zero. The top doesn't go to zero. Since the fraction is positive on both sides of zero, the limit is positive infinity.
For the second one:
The limit of [(x^2-2x)/(x^2-4x+4)] as x-> 2, from the left:
If you try to plug in 2 directly, the top and bottom both go to zero. So we have to do something. Factoring comes to mind. You can factor (x-2) out of the top and the bottom. (The bottom factors to (x-2)(x-2)). So then the limit simplifies to:
lim[x->2-] (x/(x-2)) = The top doesn't go to zero, the bottom does. As we approach from the left, x-2 is negative, so the limit is negative infinity.
