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Math Help - Finding a value of an expression (fraction)

  1. #1
    Junior Member lanierms's Avatar
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    Finding a value of an expression (fraction)

    a, b, c are positive real numbers.

    If they satisfy the equations:

    (\frac{b}{a}+\frac{a}{b})(\frac{1}{a}+\frac{1}{b}+  \frac{1}{c})=\frac{70}{a+b+c}

    (\frac{c}{b}+\frac{b}{c})(\frac{1}{a}+\frac{1}{b}+  \frac{1}{c})=\frac{90}{a+b+c}

    (\frac{a}{c}+\frac{c}{a})(\frac{1}{a}+\frac{1}{b}+  \frac{1}{c})=\frac{110}{a+b+c}

    Find the value of

    (a+b+c)(\frac{1}{a}+\frac{1}{b}+\frac{1}{c}).
    Last edited by lanierms; February 27th 2011 at 06:34 PM.
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