2/x^2-9+5/x+3=6/x^2-9

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Solution for 2/x^2-9+5/x+3=6/x^2-9 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)

5/x+2/(x^2)-9+3 = 6/(x^2)-9 // - 6/(x^2)-9

5/x+2/(x^2)-(6/(x^2))-9+3+9 = 0

5/x+2/(x^2)-6*x^-2-9+3+9 = 0

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

t_1 = x^-1

5*t_1^1-4*t_1^2+3 = 0

5*t_1-4*t_1^2+3 = 0

DELTA = 5^2-(-4*3*4)

DELTA = 73

DELTA > 0

t_1 = (73^(1/2)-5)/(-4*2) or t_1 = (-73^(1/2)-5)/(-4*2)

t_1 = (73^(1/2)-5)/(-8) or t_1 = (73^(1/2)+5)/8

t_1 = (73^(1/2)-5)/(-8)

x^-1-((73^(1/2)-5)/(-8)) = 0

1*x^-1 = (73^(1/2)-5)/(-8) // : 1

x^-1 = (73^(1/2)-5)/(-8)

-1 < 0

1/(x^1) = (73^(1/2)-5)/(-8) // * x^1

1 = ((73^(1/2)-5)/(-8))*x^1 // : (73^(1/2)-5)/(-8)

-8*(73^(1/2)-5)^-1 = x^1

x = -8*(73^(1/2)-5)^-1

t_1 = (73^(1/2)+5)/8

x^-1-((73^(1/2)+5)/8) = 0

1*x^-1 = (73^(1/2)+5)/8 // : 1

x^-1 = (73^(1/2)+5)/8

-1 < 0

1/(x^1) = (73^(1/2)+5)/8 // * x^1

1 = ((73^(1/2)+5)/8)*x^1 // : (73^(1/2)+5)/8

8*(73^(1/2)+5)^-1 = x^1

x = 8*(73^(1/2)+5)^-1

x in { -8*(73^(1/2)-5)^-1, 8*(73^(1/2)+5)^-1 }

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