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Math Help - Simplifying the equation

  1. #1
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    Simplifying the equation

    (abc^3 + ab^3c + a^3 bc) / (a^2 + b^2 + c^2 ) = abc


    I don't understand how to show the steps to simplify this equation. Any help is well appreciated.
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  2. #2
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    Re: Simplifying the equation

    Quote Originally Posted by greengilt View Post
    (abc^3 + ab^3c + a^3 bc) / (a^2 + b^2 + c^2 ) = abc
    I don't understand how to show the steps to simplify this equation. Any help is well appreciated.
    Hint: if \frac{A}{B}=C then it must be A=BC~.
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  3. #3
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    Re: Simplifying the equation

    Another perspective, to help verify this identity (for at least one of a, b, c nonzero):
    The numerator has a common factor "abc".

    Factor this out, and you'll be left with...
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  4. #4
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    Re: Simplifying the equation

    I see the answer and what you are telling me works in my head like so:

     {ABC^3 + AB^3C + A^3BC } = ABC(A^2 + B^2 + C^2)

    However if, for example, I only had :

     {ABC^3 + AB^3C + A^3BC } \over {A^2 + B^2 + C^2}

    then when I try to simplify I get

     {ABC \cdot C^2 + ABC \cdot B^2 + ABC \cdot A^2} \over {A^2 + B^2 + C^2}

    and my answer ends up being

    3ABC

    Where am I going wrong?
    Last edited by greengilt; September 19th 2011 at 10:37 AM.
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  5. #5
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    Re: Simplifying the equation

    Like TheChaz said the numerator has a common factor "abc"

    (abc^3 + ab^3c + a^3 bc) = abc(c^2 + b^2 + a^2)
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  6. #6
    Super Member TheChaz's Avatar
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    Re: Simplifying the equation

    I'm guessing that you are going wrong in a terrible way.

    Symbolically, you could (COULD, not SHOULD!) see the C^2 on top and likewise a C^2 on bottom, and literally just erase them from the page. Same with A^2 and B^2.

    In that case, you would have ABC(eraser mark) + ABC(eraser mark) + ABC(eraser mark), all divided by (eraser mark + eraser mark + eraser mark)

    And maybe you're thinking that since you have ABC three times, that this is 3ABC.

    This is terribly wrong.

    "Cancel factors, not terms" is a concise way to avoid this problem. I'll let someone else fill in the distinction.
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