Question

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

Answer 1

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

Answer 2

What do i do next?

Answer 3

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

Answer 4

ok

Answer 5

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

Answer 6

You have to multiply by the reciprocal of x-6/x when you divide, btw. Now you have a new expression

\[\frac{(x+2)x}{(x-5)(x-6)}\]

Answer 7

i see

Answer 8

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

Answer 9

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

Answer 10

so what does x not equal?

Answer 11

\[f(x)=\frac{x+2}{x-5} \div \frac{x-6}{x}\]
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

Answer 12

0?

Answer 13

division by 0 does not give you 0

Answer 14

6?

Answer 15

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

Answer 16

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

Answer 17

so x is not 5 and 6?

Answer 18

or also?

Answer 19

there are 3 values we talked about

Answer 20

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

Answer 21

\[f(x)=\frac{x+2}{x-5} \div \frac{x-6}{x} \]
do you see an x on the bottom of the second fraction?

Answer 22

that cannot be 0 because we cannot divide by 0

Answer 23

my options are
x is not 5,6
x is not 5,0
x is not -2,6
x is not -2, 0

Answer 24

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

Answer 25

a?

Answer 26

no e

Answer 27

none of the above

Answer 28

x is cannot be 0,5,6

Answer 29

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

Answer 30

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

Answer 31

ok

Answer 32

\[f(x)=\frac{x+2}{x-5} \div \frac{x-6}{x} \\f(0)=\frac{0+2}{0-5} \div \frac{0-6}{0}=\frac{2}{-5} \div \frac{-6}{0} \text{(second fraction undefined } \\ f(5)=\frac{5+2}{5-5} \div \frac{5-6}{5} =\frac{7}{0} \div \frac{-1}{5} \text{ (first fraction undefined } \\ f(6)=\frac{6+2}{6-5} \div \frac{6-6}{6}=\frac{8}{1} \div \frac{0}{6}=8 \div 0=\frac{8}{0} \text{(again we cannot divide by 0}\]
if your teacher doesn't know write all of this out and tell you cannot divide by 0

Answer 33

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. :)

Answer 34

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

Answer 35

Ok, i will talk to her about it, thanks

Answer 36

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