(54-6x^2)/(x^3-3x-18)

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Solution for (54-6x^2)/(x^3-3x-18) equation: 


D( x )

x^3-(3*x)-18 = 0

x^3-(3*x)-18 = 0

x^3-(3*x)-18 = 0

x^3-3*x-18 = 0

x^3-3*x-18 = 0

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

1

x = 1

x^3-3*x-18 = -20

1

-1

x = -1

x^3-3*x-18 = -16

-1

2

x = 2

x^3-3*x-18 = -16

2

-2

x = -2

x^3-3*x-18 = -20

-2

3

x = 3

x^3-3*x-18 = 0

3

x-3

x^2+3*x+6

x^3-3*x-18

x-3

3*x^2-x^3

3*x^2-3*x-18

9*x-3*x^2

6*x-18

18-6*x

0

x^2+3*x+6 = 0

DELTA = 3^2-(1*4*6)

DELTA = -15

DELTA < 0

x in { 3} 

x in (-oo:3) U (3:+oo)

(54-(6*x^2))/(x^3-(3*x)-18) = 0

(54-6*x^2)/(x^3-3*x-18) = 0

x^3-3*x-18 = 0

x^3-3*x-18 = 0

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

1

x = 1

x^3-3*x-18 = -20

1

-1

x = -1

x^3-3*x-18 = -16

-1

2

x = 2

x^3-3*x-18 = -16

2

-2

x = -2

x^3-3*x-18 = -20

-2

3

x = 3

x^3-3*x-18 = 0

3

x-3

x^2+3*x+6

x^3-3*x-18

x-3

3*x^2-x^3

3*x^2-3*x-18

9*x-3*x^2

6*x-18

18-6*x

0

x^2+3*x+6 = 0

DELTA = 3^2-(1*4*6)

DELTA = -15

DELTA < 0

x in { 3} 

x-3 = 0

(54-6*x^2)/(x-3) = 0

-6*x^2 = -54 // : -6

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

x in { 3} 

x = -3

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