François Viete Going Wild

Algebra Level 5

If \(\alpha, \beta, \gamma \) are the roots of \( x^3 - x - 1 = 0 \), find \(\dfrac{1 + \alpha}{1 - \alpha} + \dfrac{1 + \beta}{1 - \beta} + \dfrac{1 + \gamma}{1 - \gamma}\).