It is true (prove it) that if a> b> 0:

1a<1b\dfrac{1}{a}< \dfrac{1}{b}



1a<1b bab<aab  b<aa>b \dfrac{1}{a}< \dfrac{1}{b} \ \\ \dfrac{b}{ab}< \dfrac{a}{ab} \ \\ \ \\ b < a \Rightarrow a > b \ \\

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