x+1/x-1=-9/x+3+8/x^2+2x-3

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Solution for x+1/x-1=-9/x+3+8/x^2+2x-3 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+1/x-1 = 2*x-9/x+8/(x^2)-3+3 // - 2*x-9/x+8/(x^2)-3+3

x-(2*x)+1/x-(-9/x)-(8/(x^2))-3-1+3 = 0

x-2*x+1/x+9*x^-1-8*x^-2-3-1+3 = 0

10*x^-1-1*x^1-8*x^-2-1*x^0 = 0

(10*x^1-1*x^3-1*x^2-8*x^0)/(x^2) = 0 // * x^4

x^2*(10*x^1-1*x^3-1*x^2-8*x^0) = 0

x^2

10*x-x^3-x^2-8 = 0

{ 1, -1, 2, -2, 4, -4, 8, -8 }

1

x = 1

10*x-x^3-x^2-8 = 0

1

x-1

8-x^2-2*x

10*x-x^3-x^2-8

x-1

x^3-x^2

10*x-2*x^2-8

2*x^2-2*x

8*x-8

8-8*x

0

8-x^2-2*x = 0

DELTA = (-2)^2-(-1*4*8)

DELTA = 36

DELTA > 0

x = (36^(1/2)+2)/(-1*2) or x = (2-36^(1/2))/(-1*2)

x = -4 or x = 2

x in { -4, 2, 1} 

x in { -4, 2, 1 }

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