Infinity is not a number, so don't think that it follows the same rules that numbers do. Where it's easy to get confused is when Infinity takes on some properties of numbers, so people have a hard time distinguishing fact from fiction.
Infinity/Infinity = Indeterminate
**Without going into detail of why this is true, think of this question: What is the ratio of real numbers between 0-1 and 0-10? There are an infinite number of real numbers between 0-1, and likewise, there are an infinite number of real numbers between 0-10, so the ratio is Infinity/Infinity. However, everyone knows that there aren't an equal amount of numbers between 0-1 and 0-10, so logically, the ratio isn't 1:1. There are different "types" of infinity-countable, uncountable, etc., so it's impossible to say that one infinity is always the same as another.
Similar logic can be applied to these other indeterminate forms:
Infinity - Infinity = Indeterminate
0^Infinity = Indeterminiate
Infinity^0 = Indeterminate
1/Infinity + 1/Infinity + 1/Infinity .... ad infinitum = Indeterminate (if I'm not mistaken)