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

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Solution for 9-x^(-2)/3+x^(-1) equation: 


D( x )

x = 0

x = 0

x = 0

x in (-oo:0) U (0:+oo)

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

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

t_1 = x^-1

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

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

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

DELTA = 13

DELTA > 0

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

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

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

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

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

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

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

-1 < 0

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

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

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

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

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

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

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

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

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

-1 < 0

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

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

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

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

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

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