Question 35
Prove the inequality for positive real numbers $x_1$, $x_2$, $\dots$, $x_n$:
$$
\frac{x_1}{x_2+x_3} + \frac{x_2}{x_3+x_4} + \dots + \frac{x_{n-2}}{x_{n-1}+x_n} + \frac{x_{n-1}}{x_n+x_1} + \frac{x_n}{x_1+x_2}
\ge \frac{x_2}{x_1+x_2} + \frac{x_3}{x_2+x_3} + \dots + \frac{x_n}{x_{n-1}+x_n} + \frac{x_1}{x_n+x_1}
$$
$$
\frac{x_1}{x_2+x_3} + \frac{x_2}{x_3+x_4} + \dots + \frac{x_{n-2}}{x_{n-1}+x_n} + \frac{x_{n-1}}{x_n+x_1} + \frac{x_n}{x_1+x_2}
\ge \frac{x_2}{x_1+x_2} + \frac{x_3}{x_2+x_3} + \dots + \frac{x_n}{x_{n-1}+x_n} + \frac{x_1}{x_n+x_1}
$$