PL-OM 1990 Problem 2

Let $x_1, x_2, . . . , x_n$ be positive numbers. Prove that

$$\sum\limits_{i=1}^n \dfrac{x_i ^2}{x_i ^2+x_{i+1}x_{i+2}} \leq n-1$$

Where $x_{n+1}=x_1$ and $x_{n+2}=x_2$ .