If you're dividing by infinities you're doing a meaningless operation, one which can't be determined, unless you know the nature of how those infinities arise. For instance a sphere whose radius is expanding as time passes will eventually being infinite in size after an infinite time, that does not mean the volume or radius divided by the time, which would produce the rate or speed of expansion, would be "1", it would not even necessarily be a constant increase in volume or radius and certainly wouldn't be zero.

If you didn't know the way in which such an expansion occurred, say because you popped into a space that was already truly massive in size and age, you'd have no way to measure how it increased in size with time and thus the answer 'could not be determined' and so on. A given volume or radius might, for instance, actually expand faster as time goes on, thus leading to a value for expansion that wasn't 0, 1, or some constant value between zero and infinity but some variable instead.