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

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

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

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

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

t_1 = x^-1

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

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

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

DELTA = 117

DELTA > 0

t_1 = (117^(1/2)+9)/(2*9) or t_1 = (9-117^(1/2))/(2*9)

t_1 = (3*13^(1/2)+9)/18 or t_1 = (9-3*13^(1/2))/18

t_1 = (9-3*13^(1/2))/18

x^-1-((9-3*13^(1/2))/18) = 0

1*x^-1 = (9-3*13^(1/2))/18 // : 1

x^-1 = (9-3*13^(1/2))/18

-1 < 0

1/(x^1) = (9-3*13^(1/2))/18 // * x^1

1 = ((9-3*13^(1/2))/18)*x^1 // : (9-3*13^(1/2))/18

18*(9-3*13^(1/2))^-1 = x^1

x = 18*(9-3*13^(1/2))^-1

t_1 = (3*13^(1/2)+9)/18

x^-1-((3*13^(1/2)+9)/18) = 0

1*x^-1 = (3*13^(1/2)+9)/18 // : 1

x^-1 = (3*13^(1/2)+9)/18

-1 < 0

1/(x^1) = (3*13^(1/2)+9)/18 // * x^1

1 = ((3*13^(1/2)+9)/18)*x^1 // : (3*13^(1/2)+9)/18

18*(3*13^(1/2)+9)^-1 = x^1

x = 18*(3*13^(1/2)+9)^-1

x in { 18*(9-3*13^(1/2))^-1, 18*(3*13^(1/2)+9)^-1 }

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