Nesbitt inequality symmetric proof
Solution 1:
Hint: There are six terms on expansion of $\displaystyle \sum_{cyc} \frac{x+z}y = \sum_{sym} \frac{x}y$, just do AM-GM on the whole lot!
Hint: There are six terms on expansion of $\displaystyle \sum_{cyc} \frac{x+z}y = \sum_{sym} \frac{x}y$, just do AM-GM on the whole lot!