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D( z )
z-1 = 0
z+1 = 0
z^2-1 = 0
z-1 = 0
z-1 = 0
z-1 = 0 // + 1
z = 1
z+1 = 0
z+1 = 0
z+1 = 0 // - 1
z = -1
z^2-1 = 0
z^2-1 = 0
1*z^2 = 1 // : 1
z^2 = 1
z^2 = 1 // ^ 1/2
abs(z) = 1
z = 1 or z = -1
z in (-oo:-1) U (-1:1) U (1:+oo)
z/(z-1)+3/(z+1) = 2/(z^2-1) // - 2/(z^2-1)
z/(z-1)+3/(z+1)-(2/(z^2-1)) = 0
z/(z-1)+3/(z+1)-2*(z^2-1)^-1 = 0
z/(z-1)+3/(z+1)-2/(z^2-1) = 0
(z*(z+1)*(z^2-1))/((z-1)*(z+1)*(z^2-1))+(3*(z-1)*(z^2-1))/((z-1)*(z+1)*(z^2-1))+(-2*(z-1)*(z+1))/((z-1)*(z+1)*(z^2-1)) = 0
z*(z+1)*(z^2-1)+3*(z-1)*(z^2-1)-2*(z-1)*(z+1) = 0
z^4+4*z^3-4*z^2-2*z^2-4*z+2+3 = 0
z^4+4*z^3-6*z^2-4*z+5 = 0
z^4+4*z^3-6*z^2-4*z+5 = 0
z^4+4*z^3-6*z^2-4*z+5 = 0
{ 1, -1, 5, -5 }
1
z = 1
z^4+4*z^3-6*z^2-4*z+5 = 0
1
z-1
z^3+5*z^2-z-5
z^4+4*z^3-6*z^2-4*z+5
z-1
z^3-z^4
5*z^3-6*z^2-4*z+5
5*z^2-5*z^3
5-z^2-4*z
z^2-z
5-5*z
5*z-5
0
z^3+5*z^2-z-5 = 0
{ 1, -1, 5, -5 }
1
z = 1
z^3+5*z^2-z-5 = 0
1
z-1
z^2+6*z+5
z^3+5*z^2-z-5
z-1
z^2-z^3
6*z^2-z-5
6*z-6*z^2
5*z-5
5-5*z
0
z^2+6*z+5 = 0
DELTA = 6^2-(1*4*5)
DELTA = 16
DELTA > 0
z = (16^(1/2)-6)/(1*2) or z = (-16^(1/2)-6)/(1*2)
z = -1 or z = -5
z in { -5, -1, 1, 1}
(z+5)*(z+1)*(z-1)^2 = 0
((z+5)*(z+1)*(z-1)^2)/((z-1)*(z+1)*(z^2-1)) = 0
((z+5)*(z+1)*(z-1)^2)/((z-1)*(z+1)*(z^2-1)) = 0 // * (z-1)*(z+1)*(z^2-1)
(z+5)*(z+1)*(z-1)^2 = 0
( z+1 )
z+1 = 0 // - 1
z = -1
( z+5 )
z+5 = 0 // - 5
z = -5
( z-1 )
z-1 = 0 // + 1
z = 1
z in { -1}
z in { 1}
z = -5
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