Comments by "MC116" (@angelmendez-rivera351) on "Calculus: How to Find a Limit by Rationalizing the Numerator" video.

@kameronpeterson3601 No, that is false.
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If the numerator and denominator both approach 0, then there is never a situation where rationalization does not work. This can actually be proven. This is because if both approach 0, then, by a generalization of the fundamental theorem of algebra, they must both share some hidden common factor, and you can always cancel it. In this case, notice that x – 4 = (x + 5) – 9 = [sqrt(x + 5) – 3]·[sqrt(x + 5) + 3]. So as you can see, there is a common factor here.
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@supersid6682 No, he did it correctly. You can indeed cancel x – 4, because it is not equal to 0. It only merely approaches 0. That is why this is called a limit.
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