Polynomial Vieta

Algebra Level 2

The roots of the polynomial equation $$x^3 + 2 x^2 + 3 x + 4 = 0$$ are $$\alpha, \beta,$$ and $$\gamma$$. What is the value of

$\frac{ \alpha + \beta} { \gamma} + \frac{ \beta + \gamma} { \alpha } + \frac{ \gamma + \alpha } { \beta } ?$

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