# A Cubic Polynomial Transformed

Algebra Level 4

The Roots of the following Cubic Equation are $$\displaystyle \alpha$$, $$\displaystyle \beta$$ and $$\displaystyle \gamma$$.

$\displaystyle x^3+7x^2+2x+9=0$

Then the value of the Expression

$\displaystyle \dfrac{(3 \alpha-2)(3 \beta-2)(3 \gamma-2)}{(2+3 \alpha)(2+3 \beta)(2+3 \gamma)}$

Can be written as $$\displaystyle \dfrac{a}{b}$$, where $$\displaystyle a$$ and $$\displaystyle b$$ are coprime positive integers. Find $$\displaystyle a+b$$.

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