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Math Help - Guidelines needed

  1. #1
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    Guidelines needed

    The Problem:

    \frac {1}{a-b} - \frac {3ab}{a^3-b^3}

    What I have done:

    \frac {1}{a-b} - \frac {3ab}{a^3-b^3}

    \frac {1}{a-b} - \frac {3ab}{(a-b)(a^2+ab+b^2)}

    I found the least common factor to be (a-b)(a^2+ab+b^2)

    Then I multiplicated the first expression by a^2+ab+b^2 And therefore I have:

    \frac {1(a^2+ab+b^2)}{(a-b)(a^2+ab+b^2)} - \frac {3ab}{(a-b)(a^2+ab+b^2)}

    \frac {a^2+ab+b^2-3ab}{(a-b)(a^2+ab+b^2)}


    And now I have:

    \frac {-3ab}{a-b}


    But the book answer is \frac {a-b}{a^2+ab+b^2}

    Any guideline...???
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  2. #2
    A riddle wrapped in an enigma
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    Quote Originally Posted by Alienis Back View Post
    The Problem:

    \frac {1}{a-b} - \frac {3ab}{a^3-b^3}

    What I have done:

    \frac {1}{a-b} - \frac {3ab}{a^3-b^3}

    \frac {1}{a-b} - \frac {3ab}{(a-b)(a^2+ab+b^2)}

    I found the least common factor to be (a-b)(a^2+ab+b^2)

    Then I multiplicated the first expression by a^2+ab+b^2 And therefore I have:

    \frac {1(a^2+ab+b^2)}{(a-b)(a^2+ab+b^2)} - \frac {3ab}{(a-b)(a^2+ab+b^2)}

    \frac {a^2+ab+b^2-3ab}{(a-b)(a^2+ab+b^2)}


    And now I have:

    \frac {-3ab}{a-b}


    But the book answer is \frac {a-b}{a^2+ab+b^2}

    Any guideline...???

    Hi Alienis,

    Let's pick it up from here:


    \frac {a^2+ab+b^2-3ab}{(a-b)(a^2+ab+b^2)}

    \frac {a^2-2ab+b^2}{(a-b)(a^2+ab+b^2)}

    \frac {(a-b)(a-b)}{(a-b)(a^2+ab+b^2)}

    The (a - b) cancels out and you have:

    \frac {a-b}{a^2+ab+b^2}
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  3. #3
    Member jacs's Avatar
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    You almost had it, just the last bit is wrong

    simplify it like this
    \frac {a^2-2ab+b^2}{(a-b)(a^2+ab+b^2)}
    \frac {(a-b)^2}{(a-b)(a^2+ab+b^2)}
    = \frac {a-b}{a^2+ab+b^2}
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  4. #4
    Member jacs's Avatar
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    oh bugger, you just beat me to it
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  5. #5
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    Don't get it yet...

    And how did you turn a^2+ab+b^2-3ab into a^2-2ab+b^2?
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  6. #6
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    Quote Originally Posted by Alienis Back View Post
    And how did you turn a^2+ab+b^2-3ab into a^2-2ab+b^2?
    a^2+ab+b^2-3ab = a^2 + ab - 3ab + b^2 \, ....
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