Alpha, Beta Gamma strike again

Algebra Level 5

If α,β,γ\alpha ,\beta,\gamma are the roots of the equation x3x1=0\displaystyle x^3-x-1=0, then determine the equation whose roots are 1+α1α,1+β1β,1+γ1γ\dfrac{1+\alpha}{1-\alpha},\dfrac{1+\beta}{1-\beta},\dfrac{1+\gamma}{1-\gamma}.

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