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

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Solution for (3/x+2)-(2/x^2-4)=(1/x-2) 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)

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

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

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

2*x^-1-2*x^-2+8 = 0

t_1 = x^-1

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

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

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

DELTA = 68

DELTA > 0

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

t_1 = (2*17^(1/2)-2)/(-4) or t_1 = (-2*17^(1/2)-2)/(-4)

t_1 = (2*17^(1/2)-2)/(-4)

x^-1-((2*17^(1/2)-2)/(-4)) = 0

1*x^-1 = (2*17^(1/2)-2)/(-4) // : 1

x^-1 = (2*17^(1/2)-2)/(-4)

-1 < 0

1/(x^1) = (2*17^(1/2)-2)/(-4) // * x^1

1 = ((2*17^(1/2)-2)/(-4))*x^1 // : (2*17^(1/2)-2)/(-4)

-4*(2*17^(1/2)-2)^-1 = x^1

x = -4*(2*17^(1/2)-2)^-1

t_1 = (-2*17^(1/2)-2)/(-4)

x^-1-((-2*17^(1/2)-2)/(-4)) = 0

1*x^-1 = (-2*17^(1/2)-2)/(-4) // : 1

x^-1 = (-2*17^(1/2)-2)/(-4)

-1 < 0

1/(x^1) = (-2*17^(1/2)-2)/(-4) // * x^1

1 = ((-2*17^(1/2)-2)/(-4))*x^1 // : (-2*17^(1/2)-2)/(-4)

-4*(-2*17^(1/2)-2)^-1 = x^1

x = -4*(-2*17^(1/2)-2)^-1

x in { -4*(2*17^(1/2)-2)^-1, -4*(-2*17^(1/2)-2)^-1 }

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