1/x-1/3=1/3x

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Solution for 1/x-1/3=1/3x equation: 


D( x )

x = 0

x = 0

x = 0

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

1/x-(1/3) = (1/3)*x // - (1/3)*x

1/x-((1/3)*x)-(1/3) = 0

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

1*x^-1-1/3*x^1-1/3*x^0 = 0

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

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

x^1

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

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

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

DELTA = 13/9

DELTA > 0

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

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

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

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

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