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amonoconnor

  • one year ago

How do you simply the following expression: (((sqrt(6-x))-2)/((sqrt(3-x)-1)))*(((sqrt(3-x))+1)/((sqrt(3-x))+1))) Thank you very much! Any and all help is greatly appreciated!

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  1. Mertsj
    • one year ago
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    \[\frac{\sqrt{6-x}-2}{\sqrt{3-x}-1}\times \frac{\sqrt{3-x}+1}{\sqrt{3-x}+1}\]

  2. Mertsj
    • one year ago
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    Is that the problem?

  3. amonoconnor
    • one year ago
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    Yes!

  4. Mertsj
    • one year ago
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    In the denominator of the first fraction: is it -1or +1

  5. jackthegreatest
    • one year ago
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    well for one u can cross out the equation on the right, the top and bottom r exactly the same

  6. amonoconnor
    • one year ago
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    Shoot.. you are correct. "-1"

  7. Mertsj
    • one year ago
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    If the problem is as I have posted it the denominators are of the form (a-b)(a+b) and that is equal to a^2-b^2

  8. amonoconnor
    • one year ago
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    I know, that's the point: Multiplying by the conjugate, but I'm weary as to how to multiple that across... ?

  9. Mertsj
    • one year ago
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    So the denominator is 3-x-1or 2-x

  10. Mertsj
    • one year ago
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    now let's do the numerator multiplication:

  11. amonoconnor
    • one year ago
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    How did you get that? :/ I'm not disagreeing, I just don't know how you worked it out..

  12. Mertsj
    • one year ago
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    \[(\sqrt{6-x}-2)(\sqrt{3-x}+1)=\sqrt{(6-x)(3-x)}+\sqrt{6-x}-2\sqrt{3-x}-2\]

  13. Mertsj
    • one year ago
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    What is (a-b)(a+b)

  14. amonoconnor
    • one year ago
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    (18 - 9x + x) :)

  15. Mertsj
    • one year ago
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    Where did that come from?

  16. amonoconnor
    • one year ago
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    Isn't that what'll be under the radical, in the first term in the numerator? :/

  17. Mertsj
    • one year ago
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    It would be 18-9x+x^2

  18. amonoconnor
    • one year ago
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    Dude, I'm tired.. my bad again.

  19. Mertsj
    • one year ago
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    so put that numerator over 2-x and you are done.

  20. amonoconnor
    • one year ago
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    Can we cancel out anything else?

  21. Mertsj
    • one year ago
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    Are there any common factors?

  22. amonoconnor
    • one year ago
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    |dw:1442976045683:dw|

  23. amonoconnor
    • one year ago
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    Is this all correct, and the final version?

  24. Mertsj
    • one year ago
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    yep

  25. amonoconnor
    • one year ago
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    |dw:1442976240464:dw|

  26. amonoconnor
    • one year ago
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    This is totally wrong, right?

  27. Mertsj
    • one year ago
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    it is correct.

  28. amonoconnor
    • one year ago
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    The second version is correct as well??

  29. amonoconnor
    • one year ago
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    That was my initial, instinctual way to multiple the numerator across, but I thought for sure it was wrong, and I understand how you first showed me, foiling the polynomials UNDER the radical, getting 18 - 9x + x^2. But are you saying that my instinctual way works?

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