(x^3-6x^2-3x+18)/(x^3+2x^2-3x-6)

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Solution for (x^3-6x^2-3x+18)/(x^3+2x^2-3x-6) equation: 


D( x )

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

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

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

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

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

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

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

x^2*(x+2)-3*(x+2)

(x^2-3)*(x+2)

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x^2-3 )

1*x^2 = 3 // : 1

x^2 = 3

x^2 = 3 // ^ 1/2

abs(x) = 3^(1/2)

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

x in (-oo:-2) U (-2:-3^(1/2)) U (-3^(1/2):3^(1/2)) U (3^(1/2):+oo)

(x^3-(6*x^2)-(3*x)+18)/(x^3+2*x^2-(3*x)-6) = 0

(x^3-6*x^2-3*x+18)/(x^3+2*x^2-3*x-6) = 0

x^3-6*x^2-3*x+18 = 0

x^3-6*x^2-3*x+18 = 0

{ 1, -1, 2, -2, 3, -3, 6, -6, 9, -9, 18, -18 }

1

x = 1

x^3-6*x^2-3*x+18 = 10

1

-1

x = -1

x^3-6*x^2-3*x+18 = 14

-1

2

x = 2

x^3-6*x^2-3*x+18 = -4

2

-2

x = -2

x^3-6*x^2-3*x+18 = -8

-2

3

x = 3

x^3-6*x^2-3*x+18 = -18

3

-3

x = -3

x^3-6*x^2-3*x+18 = -54

-3

6

x = 6

x^3-6*x^2-3*x+18 = 0

6

x-6

x^2-3

x^3-6*x^2-3*x+18

x-6

6*x^2-x^3

18-3*x

3*x-18

0

x^2-3 = 0

DELTA = 0^2-(-3*1*4)

DELTA = 12

DELTA > 0

x = (12^(1/2)+0)/(1*2) or x = (0-12^(1/2))/(1*2)

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

x in { -3^(1/2), 3^(1/2), 6} 

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

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

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

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

x^2*(x+2)-3*(x+2)

(x^2-3)*(x+2)

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

( x+3^(1/2) )

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

x = -3^(1/2)

( x-3^(1/2) )

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

x = 3^(1/2)

( x-6 )

x-6 = 0 // + 6

x = 6

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

x in { 3^(1/2)} 

x = 6

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