## Bananas1234 one year ago Identify the restrictions on the domain. x+2/x-5 divided by x-6/x

1. anonymous

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

2. Bananas1234

What do i do next?

3. anonymous

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

4. Bananas1234

ok

5. anonymous

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

6. anonymous

You have to multiply by the reciprocal of x-6/x when you divide, btw. Now you have a new expression $\frac{(x+2)x}{(x-5)(x-6)}$

7. Bananas1234

i see

8. 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

9. freckles

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

10. Bananas1234

so what does x not equal?

11. 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

12. Bananas1234

0?

13. freckles

division by 0 does not give you 0

14. Bananas1234

6?

15. freckles

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

16. freckles

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

17. Bananas1234

so x is not 5 and 6?

18. freckles

or also?

19. freckles

there are 3 values we talked about

20. freckles

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

21. 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?

22. freckles

that cannot be 0 because we cannot divide by 0

23. Bananas1234

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

24. freckles

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

25. Bananas1234

a?

26. freckles

no e

27. freckles

none of the above

28. freckles

x is cannot be 0,5,6

29. Bananas1234

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

30. freckles

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

31. Bananas1234

ok

32. 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

33. 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. :)

34. freckles

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

35. Bananas1234

Ok, i will talk to her about it, thanks

36. freckles

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

37. freckles

|dw:1433461205442:dw|

38. freckles

that was the correct and totally what they had right?

39. Bananas1234

yep, thats it :)

40. freckles

41. freckles

42. Bananas1234

yeah

43. 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

44. Bananas1234

ok

45. 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

46. xapproachesinfinity

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

47. Bananas1234

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

48. Bananas1234

i ment exclude :)

49. xapproachesinfinity

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

50. Bananas1234

ok, for now i will go with 5,6

51. xapproachesinfinity

your teacher is not a mathematician lol that's why

52. Bananas1234

ha ha yeahh

53. Bananas1234

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

54. xapproachesinfinity

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

55. Bananas1234

ok thanks!