x+1/x=3/x+3

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


D( x )

x = 0

x = 0

x = 0

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

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

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

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

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

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

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

x^1

x^2-3*x-2 = 0

x^2-3*x-2 = 0

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

DELTA = 17

DELTA > 0

x = (17^(1/2)+3)/(1*2) or x = (3-17^(1/2))/(1*2)

x = (17^(1/2)+3)/2 or x = (3-17^(1/2))/2

x in { (3-17^(1/2))/2, (17^(1/2)+3)/2} 

x in { (3-17^(1/2))/2, (17^(1/2)+3)/2 }

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