Oh you totally can (as long as you're working with implied limits, which you have to if infinity is in the mix), you just have to specify if it's a positive or negative zero.
I typed up a very angry paragraph about how you can't divide by infinity either because infinity is a function within the context of algebraic math, then I realized I was wrong, which made me step back and realize how fucky it is that the only number that is weirder than 0 isn't in fact a number