# The Play of Roots

Level pending

$$x^3 +4x -1 = 0$$ has roots $$\alpha , \beta, \gamma$$ and $$6y^3 -7y^2+ 3y -1 =0$$ where $$y= \frac {1}{1+x}$$. If $\frac {(\beta+1)(\gamma+1)}{(\alpha+1)^2} + \frac {(\gamma+1)(\alpha+1)}{(\beta+1)^2} + \frac {(\alpha+1)(\beta+1)}{(\gamma+1)^2}$ can be expressed as $$\frac {a}{b}$$ where a and b are coprime integers, find $$a+b$$.

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