x+5/x^2-4

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Solution for x+5/x^2-4 equation: 


D( x )

x^2 = 0

x^2 = 0

x^2 = 0

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

x+5/(x^2)-4 = 0

1*x^1+5*x^-2-4*x^0 = 0

(1*x^3-4*x^2+5*x^0)/(x^2) = 0 // * x^4

x^2*(1*x^3-4*x^2+5*x^0) = 0

x^2

x^3-4*x^2+5 = 0

{ 1, -1, 5, -5 }

1

x = 1

x^3-4*x^2+5 = 2

1

-1

x = -1

x^3-4*x^2+5 = 0

-1

x+1

x^2-5*x+5

x^3-4*x^2+5

x+1

-x^3-x^2

5-5*x^2

5*x^2+5*x

5*x+5

-5*x-5

0

x^2-5*x+5 = 0

DELTA = (-5)^2-(1*4*5)

DELTA = 5

DELTA > 0

x = (5^(1/2)+5)/(1*2) or x = (5-5^(1/2))/(1*2)

x = (5^(1/2)+5)/2 or x = (5-5^(1/2))/2

x in { (5-5^(1/2))/2, (5^(1/2)+5)/2, -1} 

x in { (5-5^(1/2))/2, (5^(1/2)+5)/2, -1 }

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