Calculus 12 Question! Please explain the part I highlighted. Thank you. Wait for the attachment to load

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Calculus 12 Question! Please explain the part I highlighted. Thank you. Wait for the attachment to load

Mathematics
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There is the solution to the answer, but I don't understand it. Could you please explain?
When the x makes the denominator 0, it is not included in the domain. \[\frac{ 1 }{ x(x-1) }\]

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Other answers:

x=? makes it zero.
and x=1
i think the explanation you need might be just that \[(-\infty, 0)\cup (0,1)\cup (1,\infty)\] is just a really long winded way of saying all numbers except \(0\) and\(1\)
yes x-1=0 x=1
1(1-1)=0
@satellite73 right, but I don't understand how? the way it is written is confusing
@shalante I am following you. Go ahead
\[(-\infty,0)\] means \[x <0\]
meaning x can 0.0001 or -0.0001 but not at 0
(0,1) means it can be from 0.0001 to 0.9999 but not at 1 or 0
\[(1,\infty)\] means it can be from 1.0001 to infinity.
Ok and what does the U shape represent?
only 0 and 1 makes it undefined So we wont include \[x \le0\] or \[x \le 1\] U is just a set of interval
A gap between undefined values.
But in this case it has to be x cannot equal those numbers. Since any number less or more than those would be defined. Am I right?
@Shalante, one more question. If something is like x cannot equal 1, can we say the npvs or non permissible values are 1
For the domain?
Yes I believe. Like saying x cannot equal 1. So npvs of x are 1. IS it correct?
Domain has to be an interval of defined value
If it asks you for vertical asymptote, it would work.
npv's? Hmm ive never heard that before :) interesting
Yes it was in my pre-cal 11 textbook. lol
@zepdrix and @Shalante, I am fine with solving questions, but my main problem now is understnading important concepts. Can I tag you in other questions to explain something like this. If it is ok with you guys?
Yep, the name is interesting. Havent heard it in a while.
Now I want a break and play. If no one does, I will. (In like 20 minutes)
Ok thanks for help.
I don't think it was mentioned earlier, just want to add, U means union. It's like.. the sum of those intervals, is your domain|dw:1443234023659:dw|x can lie anywhere in the ( brackets .

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