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

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Solution for (1/x-3)-(2/x+3)=(1/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)

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

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

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

3-x^-1-x^-2 = 0

t_1 = x^-1

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

3-t_1^2-t_1 = 0

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

DELTA = 13

DELTA > 0

t_1 = (13^(1/2)+1)/(-1*2) or t_1 = (1-13^(1/2))/(-1*2)

t_1 = (13^(1/2)+1)/(-2) or t_1 = (1-13^(1/2))/(-2)

t_1 = (13^(1/2)+1)/(-2)

x^-1-((13^(1/2)+1)/(-2)) = 0

1*x^-1 = (13^(1/2)+1)/(-2) // : 1

x^-1 = (13^(1/2)+1)/(-2)

-1 < 0

1/(x^1) = (13^(1/2)+1)/(-2) // * x^1

1 = ((13^(1/2)+1)/(-2))*x^1 // : (13^(1/2)+1)/(-2)

-2*(13^(1/2)+1)^-1 = x^1

x = -2*(13^(1/2)+1)^-1

t_1 = (1-13^(1/2))/(-2)

x^-1-((1-13^(1/2))/(-2)) = 0

1*x^-1 = (1-13^(1/2))/(-2) // : 1

x^-1 = (1-13^(1/2))/(-2)

-1 < 0

1/(x^1) = (1-13^(1/2))/(-2) // * x^1

1 = ((1-13^(1/2))/(-2))*x^1 // : (1-13^(1/2))/(-2)

-2*(1-13^(1/2))^-1 = x^1

x = -2*(1-13^(1/2))^-1

x in { -2*(13^(1/2)+1)^-1, -2*(1-13^(1/2))^-1 }

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