(x-3)/(x^3-9x^2+24x-18)

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Solution for (x-3)/(x^3-9x^2+24x-18) equation: 


D( x )

x^3-(9*x^2)+24*x-18 = 0

x^3-(9*x^2)+24*x-18 = 0

x^3-(9*x^2)+24*x-18 = 0

x^3-9*x^2+24*x-18 = 0

x^3-9*x^2+24*x-18 = 0

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

1

x = 1

x^3-9*x^2+24*x-18 = -2

1

-1

x = -1

x^3-9*x^2+24*x-18 = -52

-1

2

x = 2

x^3-9*x^2+24*x-18 = 2

2

-2

x = -2

x^3-9*x^2+24*x-18 = -110

-2

3

x = 3

x^3-9*x^2+24*x-18 = 0

3

x-3

x^2-6*x+6

x^3-9*x^2+24*x-18

x-3

3*x^2-x^3

24*x-6*x^2-18

6*x^2-18*x

6*x-18

18-6*x

0

x^2-6*x+6 = 0

DELTA = (-6)^2-(1*4*6)

DELTA = 12

DELTA > 0

x = (12^(1/2)+6)/(1*2) or x = (6-12^(1/2))/(1*2)

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

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

x in (-oo:(6-2*3^(1/2))/2) U ((6-2*3^(1/2))/2:3) U (3:(2*3^(1/2)+6)/2) U ((2*3^(1/2)+6)/2:+oo)

(x-3)/(x^3-(9*x^2)+24*x-18) = 0

(x-3)/(x^3-9*x^2+24*x-18) = 0

x^3-9*x^2+24*x-18 = 0

x^3-9*x^2+24*x-18 = 0

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

1

x = 1

x^3-9*x^2+24*x-18 = -2

1

-1

x = -1

x^3-9*x^2+24*x-18 = -52

-1

2

x = 2

x^3-9*x^2+24*x-18 = 2

2

-2

x = -2

x^3-9*x^2+24*x-18 = -110

-2

3

x = 3

x^3-9*x^2+24*x-18 = 0

3

x-3

x^2-6*x+6

x^3-9*x^2+24*x-18

x-3

3*x^2-x^3

24*x-6*x^2-18

6*x^2-18*x

6*x-18

18-6*x

0

x^2-6*x+6 = 0

DELTA = (-6)^2-(1*4*6)

DELTA = 12

DELTA > 0

x = (12^(1/2)+6)/(1*2) or x = (6-12^(1/2))/(1*2)

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

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

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

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

x-3 = 0 // + 3

x = 3

x in { 3} 

x belongs to the empty set

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