find the range of values of values of r which satisfies the following inequality, where a, b and c are positive ra r a + rb r b + rc r c > 1

find the range of values of values of r which satisfies the following inequality, where a, b and c are positive $\frac{r}{a}$ + $\frac{r}{b}$ + $\frac{r}{c}$ > 1

Answer Details

$\frac{r}{a}$ + $\frac{r}{b}$ + $\frac{r}{c}$ > 1 = $\frac{bcr+acr+abr}{abc}$ > 1
r(bc + ac + ba > abc) = r > $\frac{abc}{bc+ac+ab}$