If a + b + c = 0, then the value of $$\left( {\frac{{a + b}}{c} + \frac{{b + c}}{a} + \frac{{c + a}}{b}} \right)$$    $$\left( {\frac{a}{{b + c}} + \frac{b}{{c + a}} + \frac{c}{{a + b}}} \right) = \,?$$

Solution (By Examveda Team)

a + b + c = 0
Have values
a = 1
b = 2
c = - 3
$$ \Rightarrow \left( {\frac{{a + b}}{c} + \frac{{b + c}}{a} + \frac{{c + a}}{b}} \right)$$     $$\left( {\frac{a}{{b + c}} + \frac{b}{{c + a}} + \frac{c}{{a + b}}} \right)$$
$$ \Rightarrow \left( {\frac{{1 + 2}}{{ - 3}} + \frac{{2 - 3}}{1} + \frac{{ - 3 + 1}}{2}} \right)$$     $$\left( {\frac{1}{{2 - 3}} + \frac{2}{{ - 3 + 1}} + \frac{{ - 3}}{{1 + 2}}} \right)$$
$$\eqalign{ & \Rightarrow \left( { - 1 - 1 - 1} \right)\left( { - 1 - 1 - 1} \right) \cr & \Rightarrow - 3 \times - 3 \cr & \Rightarrow 9 \cr} $$