z/(z-1)+4/(z+1)=2/(z^2-1)

Solution for z/(z-1)+4/(z+1)=2/(z^2-1) equation:

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)+4/(z+1) = 2/(z^2-1) // - 2/(z^2-1)

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

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

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

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

z^4+5*z^3-5*z^2-2*z^2-5*z+2+4 = 0

z^4+5*z^3-7*z^2-5*z+6 = 0

z^4+5*z^3-7*z^2-5*z+6 = 0

z^4+5*z^3-7*z^2-5*z+6 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

z = 1

z^4+5*z^3-7*z^2-5*z+6 = 0

1

z-1

z^3+6*z^2-z-6

z^4+5*z^3-7*z^2-5*z+6

z-1

z^3-z^4

6*z^3-7*z^2-5*z+6

6*z^2-6*z^3

6-z^2-5*z

z^2-z

6-6*z

6*z-6

0

z^3+6*z^2-z-6 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

z = 1

z^3+6*z^2-z-6 = 0

1

z-1

z^2+7*z+6

z^3+6*z^2-z-6

z-1

z^2-z^3

7*z^2-z-6

7*z-7*z^2

6*z-6

6-6*z

0

z^2+7*z+6 = 0

DELTA = 7^2-(1*4*6)

DELTA = 25

DELTA > 0

z = (25^(1/2)-7)/(1*2) or z = (-25^(1/2)-7)/(1*2)

z = -1 or z = -6

z in { -6, -1, 1, 1} 

(z+6)*(z+1)*(z-1)^2 = 0

((z+6)*(z+1)*(z-1)^2)/((z-1)*(z+1)*(z^2-1)) = 0

((z+6)*(z+1)*(z-1)^2)/((z-1)*(z+1)*(z^2-1)) = 0 // * (z-1)*(z+1)*(z^2-1)

(z+6)*(z+1)*(z-1)^2 = 0

( z+1 )

z+1 = 0 // - 1

z = -1

( z+6 )

z+6 = 0 // - 6

z = -6

( z-1 )

z-1 = 0 // + 1

z = 1

z in { -1} 

z in { 1} 

z = -6