6/x^2-9-1/x-3=1

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Solution for 6/x^2-9-1/x-3=1 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)

6/(x^2)-(1/x)-9-3 = 1 // - 1

6/(x^2)-(1/x)-9-3-1 = 0

6/(x^2)-x^-1-9-3-1 = 0

6*x^-2-x^-1-13 = 0

t_1 = x^-1

6*t_1^2-1*t_1^1-13 = 0

6*t_1^2-t_1-13 = 0

DELTA = (-1)^2-(-13*4*6)

DELTA = 313

DELTA > 0

t_1 = (313^(1/2)+1)/(2*6) or t_1 = (1-313^(1/2))/(2*6)

t_1 = (313^(1/2)+1)/12 or t_1 = (1-313^(1/2))/12

t_1 = (1-313^(1/2))/12

x^-1-((1-313^(1/2))/12) = 0

1*x^-1 = (1-313^(1/2))/12 // : 1

x^-1 = (1-313^(1/2))/12

-1 < 0

1/(x^1) = (1-313^(1/2))/12 // * x^1

1 = ((1-313^(1/2))/12)*x^1 // : (1-313^(1/2))/12

12*(1-313^(1/2))^-1 = x^1

x = 12*(1-313^(1/2))^-1

t_1 = (313^(1/2)+1)/12

x^-1-((313^(1/2)+1)/12) = 0

1*x^-1 = (313^(1/2)+1)/12 // : 1

x^-1 = (313^(1/2)+1)/12

-1 < 0

1/(x^1) = (313^(1/2)+1)/12 // * x^1

1 = ((313^(1/2)+1)/12)*x^1 // : (313^(1/2)+1)/12

12*(313^(1/2)+1)^-1 = x^1

x = 12*(313^(1/2)+1)^-1

x in { 12*(1-313^(1/2))^-1, 12*(313^(1/2)+1)^-1 }

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