If the system of equations $x+ay+az=0,bx+y+bz=0$ and $cx+cy+z=0$ where $a,b,c$ are non-zero ,non unity has a non-trivial solution then the value of $\large\frac{a}{1-a}+\frac{b}{1-b}+\frac{c}{1-c}$ is

Question

$\begin{array}{1 1}(A)\;-1&(B)\;0\\(C)\;1&(D)\;\large\frac{abc}{a^2+b^2+c^2}\end{array}$

Comments

From the given eqation we get,,
x(1-a)=-a(x+y+z)
=> a/(1-a)=-x/(x+y+z) ----(1)
y(1-b)=-b(x+y+z)
=> b/(1-b)=-y/(x+y+z) ----(2)
z(1-c)=-c(x+y+z)
=> c/(1-c)=-z/(x+y+z) -----(3)
adding we get,,
a/(1-a)+b/(1-b)+c/(1-c)=-(x+y+z)/(x+y+z)=-1.