11/3x-1/3=-4/x^2

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Solution for 11/3x-1/3=-4/x^2 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

(11/3)*x-(1/3) = -4/(x^2) // + -4/(x^2)

(11/3)*x-(-4/(x^2))-(1/3) = 0

(11/3)*x+4*x^-2-1/3 = 0

11/3*x^1+4*x^-2-1/3*x^0 = 0

(11/3*x^3-1/3*x^2+4*x^0)/(x^2) = 0 // * x^4

x^2*(11/3*x^3-1/3*x^2+4*x^0) = 0

x^2

(11/3)*x^3+(-1/3)*x^2+4 = 0

(11/3)*x^3+(-1/3)*x^2+4 = 0 // * 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }

1

x = 1

11*x^3-x^2+12 = 22

1

-1

x = -1

11*x^3-x^2+12 = 0

-1

x+1

11*x^2-12*x+12

11*x^3-x^2+12

x+1

-11*x^3-11*x^2

12-12*x^2

12*x^2+12*x

12*x+12

-12*x-12

0

11*x^2-12*x+12 = 0

DELTA = (-12)^2-(4*11*12)

DELTA = -384

DELTA < 0

x in { -1} 

x = -1

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