\frac{1}{4\ \omega3\ +\ 2\ \omega2\ \ \ +\ \omega}\ +\ \frac{1}{5\ \omega6\ \ +\ 3\ \omega4\ +\ 4\ \omega2}

= \frac{1}{\left(3\ +\ \ \omega2\ \ \ +\ 2\omega4\right)\omega}\ +\ \frac{1}{4+4\ \omega\ \ +4\omega2\ +\ 1\ \omega}

=\frac{1}{\left(\ \ 2\omega\ \ \ +\ \omega\right)2\omega}\ +\ \frac{1}{\left[3\ \omega2+3\omega+3+\omega2-\omega\right]\omega}

= \frac{1}{\left[1-\omega2\right]}\ +\ \frac{1}{\left[1-\omega\right]}\ ,\ \omega3=1

=\frac{\left[1-\omega\right]+1-\omega2}{1-\left(\omega2\ +\ \omega\right)+\ \omega3}=\ \frac{1+1+1}{1+1+1}=1