Question 84
Determine the smallest possible value of the expression
$$
\frac{a b+1}{a+b}+\frac{b c+1}{b+c}+\frac{c a+1}{c+a}
$$
where $a, b, c \in \mathbb{R}$ satisfy $a+b+c=-1$ and $a b c \leq -3$.
$$
\frac{a b+1}{a+b}+\frac{b c+1}{b+c}+\frac{c a+1}{c+a}
$$
where $a, b, c \in \mathbb{R}$ satisfy $a+b+c=-1$ and $a b c \leq -3$.