(x^3+3x^2-x-6)/(x-1)

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Solution for (x^3+3x^2-x-6)/(x-1) equation: 


D( x )

x-1 = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:+oo)

(x^3+3*x^2-x-6)/(x-1) = 0

x^3+3*x^2-x-6 = 0

x^3+3*x^2-x-6 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6 }

1

x = 1

x^3+3*x^2-x-6 = -3

1

-1

x = -1

x^3+3*x^2-x-6 = -3

-1

2

x = 2

x^3+3*x^2-x-6 = 12

2

-2

x = -2

x^3+3*x^2-x-6 = 0

-2

x+2

x^2+x-3

x^3+3*x^2-x-6

x+2

-x^3-2*x^2

x^2-x-6

-x^2-2*x

-3*x-6

3*x+6

0

x^2+x-3 = 0

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

DELTA = 13

DELTA > 0

x = (13^(1/2)-1)/(1*2) or x = (-13^(1/2)-1)/(1*2)

x = (13^(1/2)-1)/2 or x = (-(13^(1/2)+1))/2

x in { (-(13^(1/2)+1))/2, (13^(1/2)-1)/2, -2} 

(x+(13^(1/2)+1)/2)*(x-((13^(1/2)-1)/2))*(x+2) = 0

((x+(13^(1/2)+1)/2)*(x-((13^(1/2)-1)/2))*(x+2))/(x-1) = 0

( x+(13^(1/2)+1)/2 )

x+(13^(1/2)+1)/2 = 0 // - (13^(1/2)+1)/2

x = -((13^(1/2)+1)/2)

( x+2 )

x+2 = 0 // - 2

x = -2

( x-((13^(1/2)-1)/2) )

x-((13^(1/2)-1)/2) = 0 // + (13^(1/2)-1)/2

x = (13^(1/2)-1)/2

x in { -((13^(1/2)+1)/2), -2, (13^(1/2)-1)/2 }

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