Method 1: (the smart way)
Use L'Hopital's rule, take the derivative of your function.
1/(x+2) - 1/(x+1) = -1/(x^2+2x+2), as x goes to infinity, your function goes to zero.
Method 2: (the faster-but-may-not-always-work way)
you know that ln(infinity) = infinity, now is there a difference between X+2 and X+1 when X is infinity? no, so the answer is zero.
Now your second problem isn't as straight forward as the first, so method 1 applies there. good luck.