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Bananas1234

  • one year ago

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

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  1. anonymous
    • one year ago
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    First, didvide the two expressions: \[\Huge \frac{ \frac{ x+2 }{ x-5 } }{ \frac{ x-6 }{ x} }\]

  2. Bananas1234
    • one year ago
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    What do i do next?

  3. anonymous
    • one year ago
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    I'm trying to load it, it doesnt seem to be working

  4. Bananas1234
    • one year ago
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    ok

  5. anonymous
    • one year ago
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    \[\Large \frac{x+2}{x-5} \times \frac{x}{x-6} \]

  6. anonymous
    • one year ago
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    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
    • one year ago
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    i see

  8. anonymous
    • one year ago
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    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
    • one year ago
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    x=0 would also need to be excluded from the domain

  10. Bananas1234
    • one year ago
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    so what does x not equal?

  11. freckles
    • one year ago
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    \[f(x)=\frac{x+2}{x-5} \div \frac{x-6}{x}\] 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
    • one year ago
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    0?

  13. freckles
    • one year ago
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    division by 0 does not give you 0

  14. Bananas1234
    • one year ago
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    6?

  15. freckles
    • one year ago
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    division by 0 is not good it is undefined a/0 is undefined

  16. freckles
    • one year ago
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    anyways I hope you can see what numbers to exclude from the domain

  17. Bananas1234
    • one year ago
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    so x is not 5 and 6?

  18. freckles
    • one year ago
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    or also?

  19. freckles
    • one year ago
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    there are 3 values we talked about

  20. freckles
    • one year ago
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    2 given by the first guy and then I gave you another remember we cannot divide by 0

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

  22. freckles
    • one year ago
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    that cannot be 0 because we cannot divide by 0

  23. Bananas1234
    • one year ago
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    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
    • one year ago
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    well I would go with option e then because x cannot be 0,5,6

  25. Bananas1234
    • one year ago
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    a?

  26. freckles
    • one year ago
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    no e

  27. freckles
    • one year ago
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    none of the above

  28. freckles
    • one year ago
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    x is cannot be 0,5,6

  29. Bananas1234
    • one year ago
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    hmmm im sorry but there is only a,b,c, and d

  30. freckles
    • one year ago
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    well I would talk to your teacher because f(0) and f(5) and f(6) are all not defined

  31. Bananas1234
    • one year ago
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    ok

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

  33. Bananas1234
    • one year ago
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    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
    • one year ago
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    i guess the 5,6 one I don't know

  35. Bananas1234
    • one year ago
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    Ok, i will talk to her about it, thanks

  36. freckles
    • one year ago
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    hey and the expression was really what I wrote ,right?

  37. freckles
    • one year ago
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    |dw:1433461205442:dw|

  38. freckles
    • one year ago
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    that was the correct and totally what they had right?

  39. Bananas1234
    • one year ago
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    yep, thats it :)

  40. freckles
    • one year ago
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    err yeah weird answers

  41. freckles
    • one year ago
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    weird answer choices*

  42. Bananas1234
    • one year ago
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    yeah

  43. freckles
    • one year ago
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    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
    • one year ago
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    ok

  45. freckles
    • one year ago
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    \[\left\{ x \in \mathbb{R}: x \neq 0 \text{ and } x \neq 5 \text{ and } x \neq 6 \right\}\] means exactly what I said which was to exclude x=0,5,6

  46. xapproachesinfinity
    • one year ago
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    I also agree that 0 is excluded from the domain irrelevant answer choices!!

  47. Bananas1234
    • one year ago
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    yeah idk why they do not include the 0......

  48. Bananas1234
    • one year ago
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    i ment exclude :)

  49. xapproachesinfinity
    • one year ago
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    hmm your teacher probably just did what the gentle man above did

  50. Bananas1234
    • one year ago
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    ok, for now i will go with 5,6

  51. xapproachesinfinity
    • one year ago
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    your teacher is not a mathematician lol that's why

  52. Bananas1234
    • one year ago
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    ha ha yeahh

  53. Bananas1234
    • one year ago
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    i can let you know if it was right if you would like

  54. xapproachesinfinity
    • one year ago
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    yeah no problem! just make sure you justify the answer @freckles gave you and the reasoning behind it

  55. Bananas1234
    • one year ago
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    ok thanks!

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