How Quickly Can You Solve This?

Algebra Level 2

\[\frac{\color{purple}{b}+\color{blue}{c}}{\color{red}{a}} + \frac{\color{blue}{c}+\color{red}{a}}{\color{purple}{b}} + \frac{\color{red}{a}+\color{purple}{b}}{\color{blue}{c}} = \ ?\]

If \(\color{red}{a}+\color{purple}{b}+\color{blue}{c} = 6\) and \(\dfrac{1}{\color{red}{a}} + \dfrac{1}{\color{purple}{b}} + \dfrac{1}{\color{blue}{c}} = 2,\) find the value of the expression above.