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

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


D( x )

3*x = 0

x = 0

3*x = 0

3*x = 0

3*x = 0 // : 3

x = 0

x = 0

x = 0

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

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

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

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

t_1 = x^-1

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

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

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

DELTA = 328/9

DELTA > 0

t_1 = ((328/9)^(1/2)-2/3)/(-9*2) or t_1 = (-(328/9)^(1/2)-2/3)/(-9*2)

t_1 = ((328/9)^(1/2)-2/3)/(-18) or t_1 = ((328/9)^(1/2)+2/3)/18

t_1 = ((328/9)^(1/2)-2/3)/(-18)

x^-1-(((328/9)^(1/2)-2/3)/(-18)) = 0

1*x^-1 = ((328/9)^(1/2)-2/3)/(-18) // : 1

x^-1 = ((328/9)^(1/2)-2/3)/(-18)

-1 < 0

1/(x^1) = ((328/9)^(1/2)-2/3)/(-18) // * x^1

1 = (((328/9)^(1/2)-2/3)/(-18))*x^1 // : ((328/9)^(1/2)-2/3)/(-18)

-18*((328/9)^(1/2)-2/3)^-1 = x^1

x = -18*((328/9)^(1/2)-2/3)^-1

t_1 = ((328/9)^(1/2)+2/3)/18

x^-1-(((328/9)^(1/2)+2/3)/18) = 0

1*x^-1 = ((328/9)^(1/2)+2/3)/18 // : 1

x^-1 = ((328/9)^(1/2)+2/3)/18

-1 < 0

1/(x^1) = ((328/9)^(1/2)+2/3)/18 // * x^1

1 = (((328/9)^(1/2)+2/3)/18)*x^1 // : ((328/9)^(1/2)+2/3)/18

18*((328/9)^(1/2)+2/3)^-1 = x^1

x = 18*((328/9)^(1/2)+2/3)^-1

x in { -18*((328/9)^(1/2)-2/3)^-1, 18*((328/9)^(1/2)+2/3)^-1 }

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