# If $\omega$ is the cube root of unity then the value of $\large\frac{a\omega+b+c\omega^2}{a\omega^2+b\omega+c}+\frac{a\omega^2+b+c\omega}{a+b\omega+c\omega^2}=?$

(A) $\omega$ (B) $\omega^2$ (C) $2\omega$ (D) $2\omega^2$

Toolbox:
• $\omega^3=1$
$\large\frac{a\omega+b+c\omega^2}{a\omega^2+b\omega+c}$$=\large\frac{a\omega+b+c\omega^2}{a\omega^2+b\omega+c}\times\frac{\omega}{\omega} =\large\frac{1}{\omega}=\frac{\omega^2}{\omega^3}$$=\omega^2$