Question 160
Let $a$, $b$ and $c$ be positive real numbers. Determine the minimum value of
$$ \frac{a+3c}{a+2b+c} + \frac{4b}{a+b+2c} - \frac{8c}{a+b+3c} \text{(posed by Li Shenghong)} $$
$$ \frac{a+3c}{a+2b+c} + \frac{4b}{a+b+2c} - \frac{8c}{a+b+3c} \text{(posed by Li Shenghong)} $$