(1/x^2-81)-(3/x-9)=(1/x+9)

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Solution for (1/x^2-81)-(3/x-9)=(1/x+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)-(3/x)-81+9 = 1/x+9 // - 1/x+9

1/(x^2)-(3/x)-(1/x)-81-9+9 = 0

1/(x^2)-3*x^-1-x^-1-81-9+9 = 0

x^-2-4*x^-1-81 = 0

t_1 = x^-1

1*t_1^2-4*t_1^1-81 = 0

t_1^2-4*t_1-81 = 0

DELTA = (-4)^2-(-81*1*4)

DELTA = 340

DELTA > 0

t_1 = (340^(1/2)+4)/(1*2) or t_1 = (4-340^(1/2))/(1*2)

t_1 = (2*85^(1/2)+4)/2 or t_1 = (4-2*85^(1/2))/2

t_1 = (4-2*85^(1/2))/2

x^-1-((4-2*85^(1/2))/2) = 0

1*x^-1 = (4-2*85^(1/2))/2 // : 1

x^-1 = (4-2*85^(1/2))/2

-1 < 0

1/(x^1) = (4-2*85^(1/2))/2 // * x^1

1 = ((4-2*85^(1/2))/2)*x^1 // : (4-2*85^(1/2))/2

2*(4-2*85^(1/2))^-1 = x^1

x = 2*(4-2*85^(1/2))^-1

t_1 = (2*85^(1/2)+4)/2

x^-1-((2*85^(1/2)+4)/2) = 0

1*x^-1 = (2*85^(1/2)+4)/2 // : 1

x^-1 = (2*85^(1/2)+4)/2

-1 < 0

1/(x^1) = (2*85^(1/2)+4)/2 // * x^1

1 = ((2*85^(1/2)+4)/2)*x^1 // : (2*85^(1/2)+4)/2

2*(2*85^(1/2)+4)^-1 = x^1

x = 2*(2*85^(1/2)+4)^-1

x in { 2*(4-2*85^(1/2))^-1, 2*(2*85^(1/2)+4)^-1 }

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