\[\boxed{\text{1010.\ }\text{еуроки}\text{-}\text{ответы}\text{\ }\text{на}\text{\ }\text{пятёрку}}\]
\[a > 0,\ \ b > 0,\ \ c > 0\]
\[\frac{3}{a + b + c} < \frac{1}{a + b} + \frac{1}{b + c} +\]
\[+ \frac{1}{c + a}\]
\[\frac{1}{(a + b) + c} + \frac{1}{(b + c) + a} +\]
\[+ \frac{1}{(c + a) + b} < \frac{1}{a + b} +\]
\[+ \frac{1}{b + c} + \frac{1}{c + a}\]
\[верно,\ так\ как:\]