Suppose that $x_1, x_2, x_3, . . . x_n$ are real numbers between $0$ and $ 1$ with sum $s$. Prove that $$\prod_{i=1}^{n} \frac{x_i}{s + 1 - x_i} + \prod_{i=1}^{n} (1 - x_i) \le 1.$$
Source: New Zealand MO 2019 Round 1 p8
Tags: algebra, inequalities
Suppose that $x_1, x_2, x_3, . . . x_n$ are real numbers between $0$ and $ 1$ with sum $s$. Prove that $$\prod_{i=1}^{n} \frac{x_i}{s + 1 - x_i} + \prod_{i=1}^{n} (1 - x_i) \le 1.$$