x+2/x=x-1/x+4x+2/x^2-3x

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Solution for x+2/x=x-1/x+4x+2/x^2-3x equation: 


D( x )

x = 0

x^2 = 0

x = 0

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

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

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

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

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

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

x^2

3*x-x^3-2 = 0

{ 1, -1, 2, -2 }

1

x = 1

3*x-x^3-2 = 0

1

x-1

2-x^2-x

3*x-x^3-2

x-1

x^3-x^2

3*x-x^2-2

x^2-x

2*x-2

2-2*x

0

2-x^2-x = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)+1)/(-1*2) or x = (1-9^(1/2))/(-1*2)

x = -2 or x = 1

x in { -2, 1, 1} 

x in { -2, 1, 1 }

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