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

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Solution for (3/x-3)-(2/x+3)=(9/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)

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

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

3/x-2*x^-1-9*x^-2-3-3+9 = 0

x^-1-9*x^-2+3 = 0

t_1 = x^-1

1*t_1^1-9*t_1^2+3 = 0

t_1-9*t_1^2+3 = 0

DELTA = 1^2-(-9*3*4)

DELTA = 109

DELTA > 0

t_1 = (109^(1/2)-1)/(-9*2) or t_1 = (-109^(1/2)-1)/(-9*2)

t_1 = (109^(1/2)-1)/(-18) or t_1 = (109^(1/2)+1)/18

t_1 = (109^(1/2)-1)/(-18)

x^-1-((109^(1/2)-1)/(-18)) = 0

1*x^-1 = (109^(1/2)-1)/(-18) // : 1

x^-1 = (109^(1/2)-1)/(-18)

-1 < 0

1/(x^1) = (109^(1/2)-1)/(-18) // * x^1

1 = ((109^(1/2)-1)/(-18))*x^1 // : (109^(1/2)-1)/(-18)

-18*(109^(1/2)-1)^-1 = x^1

x = -18*(109^(1/2)-1)^-1

t_1 = (109^(1/2)+1)/18

x^-1-((109^(1/2)+1)/18) = 0

1*x^-1 = (109^(1/2)+1)/18 // : 1

x^-1 = (109^(1/2)+1)/18

-1 < 0

1/(x^1) = (109^(1/2)+1)/18 // * x^1

1 = ((109^(1/2)+1)/18)*x^1 // : (109^(1/2)+1)/18

18*(109^(1/2)+1)^-1 = x^1

x = 18*(109^(1/2)+1)^-1

x in { -18*(109^(1/2)-1)^-1, 18*(109^(1/2)+1)^-1 }

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