1/z-4+1/z+4=8/z^2-16

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Solution for 1/z-4+1/z+4=8/z^2-16 equation: 


D( z )

z^2 = 0

z = 0

z^2 = 0

z^2 = 0

1*z^2 = 0 // : 1

z^2 = 0

z = 0

z = 0

z = 0

z in (-oo:0) U (0:+oo)

1/z+1/z-4+4 = 8/(z^2)-16 // - 8/(z^2)-16

1/z+1/z-(8/(z^2))-4+4+16 = 0

1/z+1/z-8*z^-2-4+4+16 = 0

2*z^-1-8*z^-2+16 = 0

t_1 = z^-1

2*t_1^1-8*t_1^2+16 = 0

2*t_1-8*t_1^2+16 = 0

DELTA = 2^2-(-8*4*16)

DELTA = 516

DELTA > 0

t_1 = (516^(1/2)-2)/(-8*2) or t_1 = (-516^(1/2)-2)/(-8*2)

t_1 = (2*129^(1/2)-2)/(-16) or t_1 = (-2*129^(1/2)-2)/(-16)

t_1 = (2*129^(1/2)-2)/(-16)

z^-1-((2*129^(1/2)-2)/(-16)) = 0

1*z^-1 = (2*129^(1/2)-2)/(-16) // : 1

z^-1 = (2*129^(1/2)-2)/(-16)

-1 < 0

1/(z^1) = (2*129^(1/2)-2)/(-16) // * z^1

1 = ((2*129^(1/2)-2)/(-16))*z^1 // : (2*129^(1/2)-2)/(-16)

-16*(2*129^(1/2)-2)^-1 = z^1

z = -16*(2*129^(1/2)-2)^-1

t_1 = (-2*129^(1/2)-2)/(-16)

z^-1-((-2*129^(1/2)-2)/(-16)) = 0

1*z^-1 = (-2*129^(1/2)-2)/(-16) // : 1

z^-1 = (-2*129^(1/2)-2)/(-16)

-1 < 0

1/(z^1) = (-2*129^(1/2)-2)/(-16) // * z^1

1 = ((-2*129^(1/2)-2)/(-16))*z^1 // : (-2*129^(1/2)-2)/(-16)

-16*(-2*129^(1/2)-2)^-1 = z^1

z = -16*(-2*129^(1/2)-2)^-1

z in { -16*(2*129^(1/2)-2)^-1, -16*(-2*129^(1/2)-2)^-1 }

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