4/2x-1=2/x

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Solution for 4/2x-1=2/x equation: 


D( x )

x = 0

x = 0

x = 0

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

(4/2)*x-1 = 2/x // - 2/x

(4/2)*x-(2/x)-1 = 0

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

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

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

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

x^1

2*x^2-x-2 = 0

2*x^2-x-2 = 0

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

DELTA = 17

DELTA > 0

x = (17^(1/2)+1)/(2*2) or x = (1-17^(1/2))/(2*2)

x = (17^(1/2)+1)/4 or x = (1-17^(1/2))/4

x in { (1-17^(1/2))/4, (17^(1/2)+1)/4} 

x in { (1-17^(1/2))/4, (17^(1/2)+1)/4 }

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