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

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


D( x )

x = 0

x^2 = 0

x = 0

x = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

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

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

1/x+1/x-4*x^-2-2+2+4 = 0

2*x^-1-4*x^-2+4 = 0

t_1 = x^-1

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

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

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

DELTA = 68

DELTA > 0

t_1 = (68^(1/2)-2)/(-4*2) or t_1 = (-68^(1/2)-2)/(-4*2)

t_1 = (2*17^(1/2)-2)/(-8) or t_1 = (-2*17^(1/2)-2)/(-8)

t_1 = (2*17^(1/2)-2)/(-8)

x^-1-((2*17^(1/2)-2)/(-8)) = 0

1*x^-1 = (2*17^(1/2)-2)/(-8) // : 1

x^-1 = (2*17^(1/2)-2)/(-8)

-1 < 0

1/(x^1) = (2*17^(1/2)-2)/(-8) // * x^1

1 = ((2*17^(1/2)-2)/(-8))*x^1 // : (2*17^(1/2)-2)/(-8)

-8*(2*17^(1/2)-2)^-1 = x^1

x = -8*(2*17^(1/2)-2)^-1

t_1 = (-2*17^(1/2)-2)/(-8)

x^-1-((-2*17^(1/2)-2)/(-8)) = 0

1*x^-1 = (-2*17^(1/2)-2)/(-8) // : 1

x^-1 = (-2*17^(1/2)-2)/(-8)

-1 < 0

1/(x^1) = (-2*17^(1/2)-2)/(-8) // * x^1

1 = ((-2*17^(1/2)-2)/(-8))*x^1 // : (-2*17^(1/2)-2)/(-8)

-8*(-2*17^(1/2)-2)^-1 = x^1

x = -8*(-2*17^(1/2)-2)^-1

x in { -8*(2*17^(1/2)-2)^-1, -8*(-2*17^(1/2)-2)^-1 }

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