Identify the restrictions on the domain. x+2/x-5 divided by x-6/x

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- Bananas1234

Identify the restrictions on the domain. x+2/x-5 divided by x-6/x

- jamiebookeater

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- anonymous

First, didvide the two expressions:
\[\Huge \frac{ \frac{ x+2 }{ x-5 } }{ \frac{ x-6 }{ x} }\]

- Bananas1234

What do i do next?

- anonymous

I'm trying to load it, it doesnt seem to be working

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## More answers

- Bananas1234

ok

- anonymous

\[\Large \frac{x+2}{x-5} \times \frac{x}{x-6} \]

- 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

i see

- 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

x=0 would also need to be excluded from the domain

- Bananas1234

so what does x not equal?

- 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

0?

- freckles

division by 0 does not give you 0

- Bananas1234

6?

- freckles

division by 0
is not good
it is undefined
a/0 is undefined

- freckles

anyways I hope you can see what numbers to exclude from the domain

- Bananas1234

so x is not 5 and 6?

- freckles

or also?

- freckles

there are 3 values we talked about

- freckles

2 given by the first guy
and then I gave you another
remember we cannot divide by 0

- 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

that cannot be 0 because we cannot divide by 0

- 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

well I would go with option e then
because x cannot be 0,5,6

- Bananas1234

a?

- freckles

no e

- freckles

none of the above

- freckles

x is cannot be 0,5,6

- Bananas1234

hmmm im sorry but there is only a,b,c, and d

- freckles

well I would talk to your teacher because f(0) and f(5) and f(6) are all not defined

- Bananas1234

ok

- 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

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

i guess the 5,6 one
I don't know

- Bananas1234

Ok, i will talk to her about it, thanks

- freckles

hey and the expression was really what I wrote ,right?

- freckles

|dw:1433461205442:dw|

- freckles

that was the correct and totally what they had right?

- Bananas1234

yep, thats it :)

- freckles

err yeah
weird answers

- freckles

weird answer choices*

- Bananas1234

yeah

- 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

ok

- 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

I also agree that 0 is excluded from the domain
irrelevant answer choices!!

- Bananas1234

yeah idk why they do not include the 0......

- Bananas1234

i ment exclude :)

- xapproachesinfinity

hmm your teacher probably just did what the gentle man above did

- Bananas1234

ok, for now i will go with 5,6

- xapproachesinfinity

your teacher is not a mathematician lol that's why

- Bananas1234

ha ha yeahh

- Bananas1234

i can let you know if it was right if you would like

- xapproachesinfinity

yeah no problem! just make sure you justify the answer @freckles gave you
and the reasoning behind it

- Bananas1234

ok thanks!

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