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

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Solution for (2x-1/x)=1/x equation: 


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

2*x^2-2 = 0

2*x^2-2 = 0

DELTA = 0^2-(-2*2*4)

DELTA = 16

DELTA > 0

x = (16^(1/2)+0)/(2*2) or x = (0-16^(1/2))/(2*2)

x = 1 or x = -1

x in { -1, 1} 

x in { -1, 1 }

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