(5z-2)/(z^2-4)=(-5z)/(2-z)+(2)/(z+2)

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Solution for (5z-2)/(z^2-4)=(-5z)/(2-z)+(2)/(z+2) equation: 


D( z )

z+2 = 0

z^2-4 = 0

2-z = 0

z+2 = 0

z+2 = 0

z+2 = 0 // - 2

z = -2

z^2-4 = 0

z^2-4 = 0

1*z^2 = 4 // : 1

z^2 = 4

z^2 = 4 // ^ 1/2

abs(z) = 2

z = 2 or z = -2

2-z = 0

2-z = 0

2-z = 0 // - 2

-z = -2 // * -1

z = 2

z in (-oo:-2) U (-2:2) U (2:+oo)

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

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

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

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

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

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

5*z^4+5*z^3+2*z^3-18*z^2-4*z^2-20*z-8*z-8+16 = 0

5*z^4+7*z^3-22*z^2-28*z+8 = 0

5*z^4+7*z^3-22*z^2-28*z+8 = 0

5*z^4+7*z^3-22*z^2-28*z+8 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8 }

1

z = 1

5*z^4+7*z^3-22*z^2-28*z+8 = -30

1

-1

z = -1

5*z^4+7*z^3-22*z^2-28*z+8 = 12

-1

2

z = 2

5*z^4+7*z^3-22*z^2-28*z+8 = 0

2

z-2

5*z^3+17*z^2+12*z-4

5*z^4+7*z^3-22*z^2-28*z+8

z-2

10*z^3-5*z^4

17*z^3-22*z^2-28*z+8

34*z^2-17*z^3

12*z^2-28*z+8

24*z-12*z^2

8-4*z

4*z-8

0

5*z^3+17*z^2+12*z-4 = 0

{ 1, -1, 2, -2, 4, -4 }

1

z = 1

5*z^3+17*z^2+12*z-4 = 30

1

-1

z = -1

5*z^3+17*z^2+12*z-4 = -4

-1

2

z = 2

5*z^3+17*z^2+12*z-4 = 128

2

-2

z = -2

5*z^3+17*z^2+12*z-4 = 0

-2

z+2

5*z^2+7*z-2

5*z^3+17*z^2+12*z-4

z+2

-5*z^3-10*z^2

7*z^2+12*z-4

-7*z^2-14*z

-2*z-4

2*z+4

0

5*z^2+7*z-2 = 0

DELTA = 7^2-(-2*4*5)

DELTA = 89

DELTA > 0

z = (89^(1/2)-7)/(2*5) or z = (-89^(1/2)-7)/(2*5)

z = (89^(1/2)-7)/10 or z = (-(89^(1/2)+7))/10

z in { (-(89^(1/2)+7))/10, (89^(1/2)-7)/10, 2, -2} 

(z+(89^(1/2)+7)/10)*(z-((89^(1/2)-7)/10))*(z-2)*(z+2) = 0

((z+(89^(1/2)+7)/10)*(z-((89^(1/2)-7)/10))*(z-2)*(z+2))/((z^2-4)*(2-z)*(z+2)) = 0

((z+(89^(1/2)+7)/10)*(z-((89^(1/2)-7)/10))*(z-2)*(z+2))/((z^2-4)*(2-z)*(z+2)) = 0 // * (z^2-4)*(2-z)*(z+2)

(z+(89^(1/2)+7)/10)*(z-((89^(1/2)-7)/10))*(z-2)*(z+2) = 0

( z+(89^(1/2)+7)/10 )

z+(89^(1/2)+7)/10 = 0 // - (89^(1/2)+7)/10

z = -((89^(1/2)+7)/10)

( z+2 )

z+2 = 0 // - 2

z = -2

( z-((89^(1/2)-7)/10) )

z-((89^(1/2)-7)/10) = 0 // + (89^(1/2)-7)/10

z = (89^(1/2)-7)/10

( z-2 )

z-2 = 0 // + 2

z = 2

z in { -2} 

z in { 2} 

z in { -((89^(1/2)+7)/10), (89^(1/2)-7)/10 }

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