Given $a>b>0$
How can I prove that $\frac{1}{b} >\frac{1}{a}$ or in other words $b^{-1}>a^{-1}$
Thanks.
Given $a>b>0$
How can I prove that $\frac{1}{b} >\frac{1}{a}$ or in other words $b^{-1}>a^{-1}$
Thanks.
$a>b>0$ or, $a-b>0$, dividing by $ab>0$, you will get:
$\frac{a-b}{ab}=\frac{1}{b}-\frac{1}{a}>0$
You can start from $a-b \gt 0$, divide by $ab$, and ...