Question 185
Find the largest possible value of the expression
$$
\frac{a+b-c}{a^3+b^3+abc} + \frac{b+c-a}{b^3+c^3+abc} + \frac{c+a-b}{c^3+a^3+abc},
$$
where $a$, $b$, $c$ are positive real numbers such that $a + b + c \ge \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$.
$$
\frac{a+b-c}{a^3+b^3+abc} + \frac{b+c-a}{b^3+c^3+abc} + \frac{c+a-b}{c^3+a^3+abc},
$$
where $a$, $b$, $c$ are positive real numbers such that $a + b + c \ge \frac{1}{a} + \frac{1}{b} + \frac{1}{c}$.