if ` alpha, beta, gamma ` are the roots of ` x^(3) + x^(2)+x + 9=0` , then find the equation whose roots are `(alpha +1)/(alpha -1) , (beta+1)/(beta -1), (gamma+1)/(gamma -1)`

Explanation

Let ` y = ( x + 1)/(x -1) Rightarrow x= ( y +1)/( y-1)`
Hence, to obtained new equation replace x by ` (x +1)/(x -1)` which is given by
`((x+1)/(x-1))^(2) + ((x+1)/(x-1))+9=0`
`(x+1)^(3)+ (x+1)^(2) (x-1)+ (x+1) (x-1)^(2) + 9 (x-1)^(3) =0`
` Rightarrow 12x^(3)-24x^(2) + 28x -8 =0`
` Rightarrow 3x^(3) -6x^(2) + 7x -2=0`