Bananas1234
  • Bananas1234
Identify the restrictions on the domain. x+2/x-5 divided by x-6/x
Mathematics
  • Stacey Warren - Expert brainly.com
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
First, didvide the two expressions: \[\Huge \frac{ \frac{ x+2 }{ x-5 } }{ \frac{ x-6 }{ x} }\]
Bananas1234
  • Bananas1234
What do i do next?
anonymous
  • anonymous
I'm trying to load it, it doesnt seem to be working

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Bananas1234
  • Bananas1234
ok
anonymous
  • anonymous
\[\Large \frac{x+2}{x-5} \times \frac{x}{x-6} \]
anonymous
  • anonymous
You have to multiply by the reciprocal of x-6/x when you divide, btw. Now you have a new expression \[\frac{(x+2)x}{(x-5)(x-6)}\]
Bananas1234
  • Bananas1234
i see
anonymous
  • anonymous
The restrictions of the domain of the function basically mean what number we cannot plug into our equation (what makes the denominator 0 or what makes the numerator unrea, so if there was a sqrt up there, what makes a negative number, but here isn't one so we don;t have to worry about the numerator). Setting the denominator equal to 0 we get (x-5)(x-6)=0 x=5 x=6 These are your restrcitions
freckles
  • freckles
x=0 would also need to be excluded from the domain
Bananas1234
  • Bananas1234
so what does x not equal?
freckles
  • freckles
\[f(x)=\frac{x+2}{x-5} \div \frac{x-6}{x}\] like for example if you plug in 0 \[f(0)=\frac{0+2}{0-5} \div \frac{0-6}{0}\] what would you say that output is
Bananas1234
  • Bananas1234
0?
freckles
  • freckles
division by 0 does not give you 0
Bananas1234
  • Bananas1234
6?
freckles
  • freckles
division by 0 is not good it is undefined a/0 is undefined
freckles
  • freckles
anyways I hope you can see what numbers to exclude from the domain
Bananas1234
  • Bananas1234
so x is not 5 and 6?
freckles
  • freckles
or also?
freckles
  • freckles
there are 3 values we talked about
freckles
  • freckles
2 given by the first guy and then I gave you another remember we cannot divide by 0
freckles
  • freckles
\[f(x)=\frac{x+2}{x-5} \div \frac{x-6}{x} \] do you see an x on the bottom of the second fraction?
freckles
  • freckles
that cannot be 0 because we cannot divide by 0
Bananas1234
  • Bananas1234
my options are x is not 5,6 x is not 5,0 x is not -2,6 x is not -2, 0
freckles
  • freckles
well I would go with option e then because x cannot be 0,5,6
Bananas1234
  • Bananas1234
a?
freckles
  • freckles
no e
freckles
  • freckles
none of the above
freckles
  • freckles
x is cannot be 0,5,6
Bananas1234
  • Bananas1234
hmmm im sorry but there is only a,b,c, and d
freckles
  • freckles
well I would talk to your teacher because f(0) and f(5) and f(6) are all not defined
Bananas1234
  • Bananas1234
ok
freckles
  • freckles
\[f(x)=\frac{x+2}{x-5} \div \frac{x-6}{x} \\f(0)=\frac{0+2}{0-5} \div \frac{0-6}{0}=\frac{2}{-5} \div \frac{-6}{0} \text{(second fraction undefined } \\ f(5)=\frac{5+2}{5-5} \div \frac{5-6}{5} =\frac{7}{0} \div \frac{-1}{5} \text{ (first fraction undefined } \\ f(6)=\frac{6+2}{6-5} \div \frac{6-6}{6}=\frac{8}{1} \div \frac{0}{6}=8 \div 0=\frac{8}{0} \text{(again we cannot divide by 0}\] if your teacher doesn't know write all of this out and tell you cannot divide by 0
Bananas1234
  • Bananas1234
ok, thank you for the info. what option would you go with. none of them seem to be completely correct, but i have to chose one, and then i will talk to my teacher about it later. :)
freckles
  • freckles
i guess the 5,6 one I don't know
Bananas1234
  • Bananas1234
Ok, i will talk to her about it, thanks
freckles
  • freckles
hey and the expression was really what I wrote ,right?
freckles
  • freckles
|dw:1433461205442:dw|
freckles
  • freckles
that was the correct and totally what they had right?
Bananas1234
  • Bananas1234
yep, thats it :)
freckles
  • freckles
err yeah weird answers
freckles
  • freckles
weird answer choices*
Bananas1234
  • Bananas1234
yeah
freckles
  • freckles
http://www.wolframalpha.com/input/?i=domain+of+%28x%2B2%29%2F%28x-5%29+divided+by+%28x-6%29%2Fx if you still have any doubt you can always look here for a second opinion
Bananas1234
  • Bananas1234
ok
freckles
  • freckles
\[\left\{ x \in \mathbb{R}: x \neq 0 \text{ and } x \neq 5 \text{ and } x \neq 6 \right\}\] means exactly what I said which was to exclude x=0,5,6
xapproachesinfinity
  • xapproachesinfinity
I also agree that 0 is excluded from the domain irrelevant answer choices!!
Bananas1234
  • Bananas1234
yeah idk why they do not include the 0......
Bananas1234
  • Bananas1234
i ment exclude :)
xapproachesinfinity
  • xapproachesinfinity
hmm your teacher probably just did what the gentle man above did
Bananas1234
  • Bananas1234
ok, for now i will go with 5,6
xapproachesinfinity
  • xapproachesinfinity
your teacher is not a mathematician lol that's why
Bananas1234
  • Bananas1234
ha ha yeahh
Bananas1234
  • Bananas1234
i can let you know if it was right if you would like
xapproachesinfinity
  • xapproachesinfinity
yeah no problem! just make sure you justify the answer @freckles gave you and the reasoning behind it
Bananas1234
  • Bananas1234
ok thanks!

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