Does 0/0 always give you a 'hole' on the graph? Precalcuclus

This precalculus tutorial covers finding the vertical asymptotes of a rational function and finding the holes of a rational function. We first set the denominator equal to 0 in order to find the candidates for the vertical asymptotes and the holes. Remember, "nonzero/0" gives you a vertical asymptote, and "0/0 from the original and no nonzero/0 from the reduced" gives you a hole.

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#math #algebra #mathbasics

0:00 How to find vertical asymptotes and holes on the graph?
5:41 0/0 but still gives you a vertical asymptote

[MulunehMuluneh-mo]

What a master of exchanging markers....😮

[simplysophy]

Tell me why it took me 2 semesters to figure this out and now i clicked on this video and i FINALLY understand this in 8 mins………. Wow. I’m convinced Professors are gatekeeping. Thanks bro ✊🏻 you the goat fr

[thebingus]

Thank you king!!! Helping me pass my college algebra class !!!

[Rayanisno.okd]

OMG NOW EVERYTHING IS SEEMS EAZIER THANK YOU ❤

[OptimusPhillip]

First, I factored the denominator to find the poles of this function. I got x = -1 and x = 4.
Then, I factored the numerator to see if it shared any zeros with the denominator. I found that both the top and bottom were 0 at x = -1. So I did zero-pole cancellation, and plugged -1 into the cancelled function to see if it approached a finite value. I found that the function had a hole at (-1, 0.4).
So the function has a vertical asymptote at x = 4, and a hole at x = -1

[ManjulaMathew-wbzn]

The easier way to explain hole at x=a is if direct substitution creates 0/0 and the limit as x->a is finite. If the limit is infinite it becomes an asymptote regardless of the numerator being zero or not.

[annfyannfyud]

Thanks!! I was looking for solution when both sides of equation can't be zero. I know this one original is L'Hôpital way

[nyandyn]

Somehow I find L'Hôpital way more straightforward than factoring and reduction 😅

[Sgth]

well now I know why there's a hole. 0/0