(2/x-2)+(3/x+2)=(8/x^2-4)

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Solution for (2/x-2)+(3/x+2)=(8/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)

2/x+3/x-2+2 = 8/(x^2)-4 // - 8/(x^2)-4

2/x+3/x-(8/(x^2))-2+2+4 = 0

2/x+3/x-8*x^-2-2+2+4 = 0

5*x^-1-8*x^-2+4 = 0

t_1 = x^-1

5*t_1^1-8*t_1^2+4 = 0

5*t_1-8*t_1^2+4 = 0

DELTA = 5^2-(-8*4*4)

DELTA = 153

DELTA > 0

t_1 = (153^(1/2)-5)/(-8*2) or t_1 = (-153^(1/2)-5)/(-8*2)

t_1 = (3*17^(1/2)-5)/(-16) or t_1 = (-3*17^(1/2)-5)/(-16)

t_1 = (3*17^(1/2)-5)/(-16)

x^-1-((3*17^(1/2)-5)/(-16)) = 0

1*x^-1 = (3*17^(1/2)-5)/(-16) // : 1

x^-1 = (3*17^(1/2)-5)/(-16)

-1 < 0

1/(x^1) = (3*17^(1/2)-5)/(-16) // * x^1

1 = ((3*17^(1/2)-5)/(-16))*x^1 // : (3*17^(1/2)-5)/(-16)

-16*(3*17^(1/2)-5)^-1 = x^1

x = -16*(3*17^(1/2)-5)^-1

t_1 = (-3*17^(1/2)-5)/(-16)

x^-1-((-3*17^(1/2)-5)/(-16)) = 0

1*x^-1 = (-3*17^(1/2)-5)/(-16) // : 1

x^-1 = (-3*17^(1/2)-5)/(-16)

-1 < 0

1/(x^1) = (-3*17^(1/2)-5)/(-16) // * x^1

1 = ((-3*17^(1/2)-5)/(-16))*x^1 // : (-3*17^(1/2)-5)/(-16)

-16*(-3*17^(1/2)-5)^-1 = x^1

x = -16*(-3*17^(1/2)-5)^-1

x in { -16*(3*17^(1/2)-5)^-1, -16*(-3*17^(1/2)-5)^-1 }

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