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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.
\[\frac{ 1 }{ x(x-1) }\]

x=? makes it zero.

and x=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

\[(-\infty,0)\]
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?

A gap between undefined values.

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

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.