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Given $a>b>0$

How can I prove that $\frac{1}{b} >\frac{1}{a}$ or in other words $b^{-1}>a^{-1}$

Thanks.

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$a>b>0$ or, $a-b>0$, dividing by $ab>0$, you will get:

$\frac{a-b}{ab}=\frac{1}{b}-\frac{1}{a}>0$

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You can start from $a-b \gt 0$, divide by $ab$, and ...

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    Or just divide the original given by $ab$ ...2012-04-02