If someone could just walk me through figuring out this question, I'd appreciate it.
Let N be a natural number. Which of the following is always a natural number?
a) N/N+1
b) N+1/N
c) (N^2 + 3N + 2)/(N+1)
d) (N^2+2N)/(N^2)

Question

If someone could just walk me through figuring out this question, I'd appreciate it. 
Let N be a natural number. Which of the following is always a natural number?
a) N/N+1
b) N+1/N
c) (N^2 + 3N + 2)/(N+1)
d) (N^2+2N)/(N^2)

anonymous · Answer

The explanation says that the answer is c, because If you factor the top (N+2)(N+1)/N+1 the N+1 cancels itself out and it ends up as N+2. 
I'm just confused because you can use the cancel out method on almost all the answers and I think they would also be natural numbers? For example:
a) N/N+1 = 1 when you cancel out the N. 1 is always a natural number, so why wouldn't it work?
b) Same goes for b, N+1/N = 1 when you cancel out N. 
Maybe it's that I don't understand the rules that have to do with canceling out numbers? I would really appreciate some kind of explanation. thanks!