Question 68
Let $a, b, c$ be positive real numbers. Prove that
$$
\begin{aligned}
\frac{1}{a+b+\frac{1}{a b c}+1}+ & \frac{1}{b+c+\frac{1}{a b c}+1}+\frac{1}{c+a+\frac{1}{a b c}+1} \\
& \leq \frac{a+b+c}{a+b+c+1}
\end{aligned}
$$
$$
\begin{aligned}
\frac{1}{a+b+\frac{1}{a b c}+1}+ & \frac{1}{b+c+\frac{1}{a b c}+1}+\frac{1}{c+a+\frac{1}{a b c}+1} \\
& \leq \frac{a+b+c}{a+b+c+1}
\end{aligned}
$$