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Simplify fraction

  1. Jan 19, 2012 #1
    1. The problem statement, all variables and given/known data
    Simplify

    [tex]\frac{2}{49^{1/3}+7^{1/3}+1}[/tex]


    2. Relevant equations



    3. The attempt at a solution
    I can simplify
    [tex]\frac{2}{49^{1/3}+7^{1/3}}[/tex]

    but I don't have idea how to do this one..

    EDIT: I have found it. No need to reply this. Thanks :)
     
    Last edited: Jan 19, 2012
  2. jcsd
  3. Jan 19, 2012 #2

    SammyS

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    I see that you have found it, but for others looking later:

    Multiply the numerator & denominator by [itex]\displaystyle (7^{1/3}-1)[/itex]
     
  4. Jan 20, 2012 #3
    I did it another way but let discuss your way. I drop the numerator because we only concern about the denominator.

    After multiplying it with 71/3 - 1, I get:
    491/3 . 71/3 - 491/3 + 72/3 - 1

    I think I have to multiply the denominator with another term but I can't find it..
     
  5. Jan 20, 2012 #4

    SammyS

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    49=72 so the denominator becomes 6 .

    491/3 ∙ 71/3 - 491/3 + 72/3 - 1

    = 72/3 ∙ 71/3 - 72/3 + 72/3 - 1

    = 7 - 1
     
    Last edited: Jan 20, 2012
  6. Jan 20, 2012 #5
    It really didn't cross my mind; multiplying with (71/3 - 1) will directly give the answer. Your method is much simpler than mine. I should have noticed the pattern a^2 + a + 1 in the denominator, which can be simplified by multiplying it with (a - 1)

    Thanks :)
     
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