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Math Help - Common Denominator ?

  1. #1
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    Common Denominator ?

    How do I do this?

    (1/ 3x^(2/3)) + (2/3x^(5/3))

    thanks
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  2. #2
    MHF Contributor Siron's Avatar
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    Re: Common Denominator ?

    I guess this is the exercice:
    \frac{1}{3\cdot x^{\frac{2}{3}}}+\frac{2}{3\cdot x^{\frac{5}{3}}}
    ?
    Write:
    3x^{\frac{5}{3}}=3x^{\frac{2}{3}}.x^{\frac{3}{3}}=  3x^{\frac{2}{3}}.x

    Can you now finish it? ...
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  3. #3
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    Re: Common Denominator ?

    sorry but can you please clarify?

    I still don't understand
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  4. #4
    MHF Contributor Siron's Avatar
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    Re: Common Denominator ?

    Yes, but I edited my post, because there was a mistake in it.
    I just used the basic rule:
    a^x\cdot a^y=a^{x+y}

    It also important, is it:
    (3x)^{\frac{5}{3}} or 3\cdot x^{\frac{5}{3}}
    I think the second one. Can you confirm this? ...
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  5. #5
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    Re: Common Denominator ?

    The original problem was taking the derivative of x^(1/3) - x^(-2/3)

    so

    (1/3)x^(1/3) - (-2/3)x^(-5/3)



    Would I have to multiply (1/ 3x^(2/3)) by x^(3/3) to get it to make it the same denominator right?
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  6. #6
    MHF Contributor Siron's Avatar
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    Re: Common Denominator ?

    You made a mistake in your derivative, but in your first post it was correct so I guess you didn't see it:
    D\left(x^{\frac{1}{3}}\right)=\frac{1}{3}x^{\frac{-2}{3}}
    So you get indeed:
    \frac{1}{3\cdot x^{\frac{2}{3}}}+\frac{2}{3\cdot x^{\frac{5}{3}}}=\frac{1}{3} \left(\frac{1}{x^{\frac{2}{3}}}+\frac{2}{x^{\frac{  5}{3}}} \right)
    Now, you can wright, like I said before:
    x^{\frac{5}{3}}=x^{\frac{2}{3}}\cdot x
    So you get:
    \frac{1}{3} \left(\frac{1}{x^{\frac{2}{3}}}+\frac{2}{x^{\frac{  2}{3}}\cdot x}\right)
    Now if you multiply the left fraction with x in the numerator and denominator you'll get the same denominator as the right fraction, so:
    ...=\frac{1}{3} \left(\frac{x}{x^{\frac{5}{3}}}+\frac{2}{x^{\frac{  5}{3}}}\right)=\frac{2+x}{3\cdot x^{\frac{5}{3}}}
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