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

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Solution for x/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)

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

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

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

6*x^-1-6*x^-2+3 = 0

t_1 = x^-1

6*t_1^1-6*t_1^2+3 = 0

6*t_1-6*t_1^2+3 = 0

DELTA = 6^2-(-6*3*4)

DELTA = 108

DELTA > 0

t_1 = (108^(1/2)-6)/(-6*2) or t_1 = (-108^(1/2)-6)/(-6*2)

t_1 = (6*3^(1/2)-6)/(-12) or t_1 = (-6*3^(1/2)-6)/(-12)

t_1 = (6*3^(1/2)-6)/(-12)

x^-1-((6*3^(1/2)-6)/(-12)) = 0

1*x^-1 = (6*3^(1/2)-6)/(-12) // : 1

x^-1 = (6*3^(1/2)-6)/(-12)

-1 < 0

1/(x^1) = (6*3^(1/2)-6)/(-12) // * x^1

1 = ((6*3^(1/2)-6)/(-12))*x^1 // : (6*3^(1/2)-6)/(-12)

-12*(6*3^(1/2)-6)^-1 = x^1

x = -12*(6*3^(1/2)-6)^-1

t_1 = (-6*3^(1/2)-6)/(-12)

x^-1-((-6*3^(1/2)-6)/(-12)) = 0

1*x^-1 = (-6*3^(1/2)-6)/(-12) // : 1

x^-1 = (-6*3^(1/2)-6)/(-12)

-1 < 0

1/(x^1) = (-6*3^(1/2)-6)/(-12) // * x^1

1 = ((-6*3^(1/2)-6)/(-12))*x^1 // : (-6*3^(1/2)-6)/(-12)

-12*(-6*3^(1/2)-6)^-1 = x^1

x = -12*(-6*3^(1/2)-6)^-1

x in { -12*(6*3^(1/2)-6)^-1, -12*(-6*3^(1/2)-6)^-1 }

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