2/3x-1=1/x

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Solution for 2/3x-1=1/x equation:


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

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

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

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

DELTA = 11/3

DELTA > 0

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

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

x in { 3/4*(1-(11/3)^(1/2)), 3/4*((11/3)^(1/2)+1)}

x in { 3/4*(1-(11/3)^(1/2)), 3/4*((11/3)^(1/2)+1) }

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