BALKAN-SL 2020 A2

Given are positive reals $a, b, c$ , such that $\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=3$ . Prove that $\frac{\sqrt{a+\frac{b}{c}}+\sqrt{b+\frac{c}{a}}+\sqrt{c+\frac{a}{b}}}{3}\leq \frac{a+b+c-1}{\sqrt{2}}$ .

Albania