Question

Let a, b, and c be positive real numbers such that abc = 1. Prove that
\[\ \frac {ab}{a^5 + b^5 + ab} + \frac {bc}{b^5 + c^5 + bc} + \frac {ca}{c^5 + a^5 + ca} \le 1 \]

Answer 1

Have you tried adding the fractions and simplifying?