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Thread: Simplification

  1. #1
    Junior Member
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    Simplification

    Hello

    How would one get from



    $\displaystyle
    \frac{x(1-\frac{4}{x})-(x-4\ln(x))}{1-\frac{4}{x}}
    $

    To

    $\displaystyle
    \frac{4x(1-\ln(x))}{4-x}
    $
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  2. #2
    Super Member

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    Lexington, MA (USA)
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    Hello, macca101!

    Did you try any algebra on it?



    How would one get from: $\displaystyle \frac{x(1-\frac{4}{x})-(x-4\ln(x))}{1-\frac{4}{x}}$ to $\displaystyle \frac{4x(1-\ln(x))}{4-x}$

    Did you simplify the numerator?
    . . $\displaystyle x\left[1 - \frac{4}{x}\right] - \left[x - 4\ln(x)\right] \;=$ $\displaystyle \;x - 4 - x + 4\ln(x) \;=\;-4 + 4\ln(x)$

    So we have: .$\displaystyle \frac{-4 + 4\ln(x)}{1 - \frac{4}{x}} $

    Multiply top and bottom by $\displaystyle x:\;\;\frac{x[-4 + 4\ln(x)]}{x - 4} $

    Factor: .$\displaystyle \frac{-4x[1 - \ln(x)]}{-(4 - x)} \;= \;\frac{4x[1 - \ln(x)]}{4 - x} $
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  3. #3
    Junior Member
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    Feb 2006
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    Quote Originally Posted by Soroban
    Hello, macca101!

    Did you try any algebra on it?


    [/size]
    Yes I did but got tied up in knots

    as usual it's obvious once you know how (kicking myself again)

    Thank You
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