(4/z-3)-(24/z^2-9)=1

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Solution for (4/z-3)-(24/z^2-9)=1 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)

4/z-(24/(z^2))-3+9 = 1 // - 1

4/z-(24/(z^2))-3-1+9 = 0

4/z-24*z^-2-3-1+9 = 0

4*z^-1-24*z^-2+5 = 0

t_1 = z^-1

4*t_1^1-24*t_1^2+5 = 0

4*t_1-24*t_1^2+5 = 0

DELTA = 4^2-(-24*4*5)

DELTA = 496

DELTA > 0

t_1 = (496^(1/2)-4)/(-24*2) or t_1 = (-496^(1/2)-4)/(-24*2)

t_1 = (4*31^(1/2)-4)/(-48) or t_1 = (-4*31^(1/2)-4)/(-48)

t_1 = (4*31^(1/2)-4)/(-48)

z^-1-((4*31^(1/2)-4)/(-48)) = 0

1*z^-1 = (4*31^(1/2)-4)/(-48) // : 1

z^-1 = (4*31^(1/2)-4)/(-48)

-1 < 0

1/(z^1) = (4*31^(1/2)-4)/(-48) // * z^1

1 = ((4*31^(1/2)-4)/(-48))*z^1 // : (4*31^(1/2)-4)/(-48)

-48*(4*31^(1/2)-4)^-1 = z^1

z = -48*(4*31^(1/2)-4)^-1

t_1 = (-4*31^(1/2)-4)/(-48)

z^-1-((-4*31^(1/2)-4)/(-48)) = 0

1*z^-1 = (-4*31^(1/2)-4)/(-48) // : 1

z^-1 = (-4*31^(1/2)-4)/(-48)

-1 < 0

1/(z^1) = (-4*31^(1/2)-4)/(-48) // * z^1

1 = ((-4*31^(1/2)-4)/(-48))*z^1 // : (-4*31^(1/2)-4)/(-48)

-48*(-4*31^(1/2)-4)^-1 = z^1

z = -48*(-4*31^(1/2)-4)^-1

z in { -48*(4*31^(1/2)-4)^-1, -48*(-4*31^(1/2)-4)^-1 }

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