Max and min part 1

$\large \frac{a}{1+bc}+\frac{b}{1+ac}+\frac{c}{1+ab}$ If $a,b$ and $c$ are non-negative reals satisfying $a^2+b^2+c^2=1$ , find the sum of the maximum and minimum value of the expression above.

Submit your answer to 3 decimal places.

• Part of the max and min