((z^2-2z-8)/(z^2-4z+4)/(z-4/z-2))

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Solution for ((z^2-2z-8)/(z^2-4z+4)/(z-4/z-2)) equation: 


D( z )

z^2-(4*z)+4 = 0

z-(4/z)-2 = 0

z = 0

z^2-(4*z)+4 = 0

z^2-(4*z)+4 = 0

z^2-4*z+4 = 0

z^2-4*z+4 = 0

DELTA = (-4)^2-(1*4*4)

DELTA = 0

z = 4/(1*2)

z = 2 or z = 2

z-(4/z)-2 = 0

z-(4/z)-2 = 0

z-4*z^-1-2 = 0

1*z^1-4*z^-1-2*z^0 = 0

(1*z^2-2*z^1-4*z^0)/(z^1) = 0 // * z^2

z^1*(1*z^2-2*z^1-4*z^0) = 0

z^1

z^2-2*z-4 = 0

z^2-2*z-4 = 0

DELTA = (-2)^2-(-4*1*4)

DELTA = 20

DELTA > 0

z = (20^(1/2)+2)/(1*2) or z = (2-20^(1/2))/(1*2)

z = (2*5^(1/2)+2)/2 or z = (2-2*5^(1/2))/2

z in { (2-2*5^(1/2))/2, (2*5^(1/2)+2)/2} 

z = 0

z = 0

z in (-oo:(2-2*5^(1/2))/2) U ((2-2*5^(1/2))/2:0) U (0:2) U (2:(2*5^(1/2)+2)/2) U ((2*5^(1/2)+2)/2:+oo)

((z^2-(2*z)-8)/(z^2-(4*z)+4))/(z-(4/z)-2) = 0

((z^2-2*z-8)/(z^2-4*z+4))/(z-4*z^-1-2) = 0

(z^2-2*z-8)/((z^2-4*z+4)*(z-4*z^-1-2)) = 0

z^2-2*z-8 = 0

z^2-2*z-8 = 0

DELTA = (-2)^2-(-8*1*4)

DELTA = 36

DELTA > 0

z = (36^(1/2)+2)/(1*2) or z = (2-36^(1/2))/(1*2)

z = 4 or z = -2

(z+2)*(z-4) = 0

z^2-4*z+4 = 0

z^2-4*z+4 = 0

DELTA = (-4)^2-(1*4*4)

DELTA = 0

z = 4/(1*2)

z = 2 or z = 2

(z-2)^2 = 0

z-4*z^-1-2 = 0

1*z^1-4*z^-1-2*z^0 = 0

(1*z^2-2*z^1-4*z^0)/(z^1) = 0 // * z^2

z^1*(1*z^2-2*z^1-4*z^0) = 0

z^1

z^2-2*z-4 = 0

z^2-2*z-4 = 0

DELTA = (-2)^2-(-4*1*4)

DELTA = 20

DELTA > 0

z = (20^(1/2)+2)/(1*2) or z = (2-20^(1/2))/(1*2)

z = (2*5^(1/2)+2)/2 or z = (2-2*5^(1/2))/2

z in { (2-2*5^(1/2))/2, (2*5^(1/2)+2)/2} 

(z-((2-2*5^(1/2))/2))*(z-((2*5^(1/2)+2)/2)) = 0

((z+2)*(z-4))/((z-2)^2*(z-((2-2*5^(1/2))/2))*(z-((2*5^(1/2)+2)/2))) = 0

( z+2 )

z+2 = 0 // - 2

z = -2

( z-4 )

z-4 = 0 // + 4

z = 4

z in { -2, 4 }

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