(x^4-x^2-12)/(x^4+2x^3-3x-6)

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Solution for (x^4-x^2-12)/(x^4+2x^3-3x-6) equation: 


D( x )

x^4+2*x^3-(3*x)-6 = 0

x^4+2*x^3-(3*x)-6 = 0

x^4+2*x^3-(3*x)-6 = 0

x^4+2*x^3-3*x-6 = 0

x^4+2*x^3-3*x-6 = 0

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

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

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

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

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x^3-3 )

1*x^3 = 3 // : 1

x^3 = 3

x^3 = 3 // ^ 1/3

x = 3^(1/3)

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

(x^4-x^2-12)/(x^4+2*x^3-(3*x)-6) = 0

(x^4-x^2-12)/(x^4+2*x^3-3*x-6) = 0

x^4-x^2-12 = 0

x^4-x^2-12 = 0

{ 1, -1, 2, -2, 3, -3, 4, -4, 6, -6, 12, -12 }

1

x = 1

x^4-x^2-12 = -12

1

-1

x = -1

x^4-x^2-12 = -12

-1

2

x = 2

x^4-x^2-12 = 0

2

x-2

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

x^4-x^2-12

x-2

2*x^3-x^4

2*x^3-x^2-12

4*x^2-2*x^3

3*x^2-12

6*x-3*x^2

6*x-12

12-6*x

0

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

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

1

x = 1

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

1

-1

x = -1

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

-1

2

x = 2

x^3+2*x^2+3*x+6 = 28

2

-2

x = -2

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

-2

x+2

x^2+3

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

x+2

-x^3-2*x^2

3*x+6

-3*x-6

0

x^2+3 = 0

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

DELTA = -12

DELTA < 0

x in { 2, -2} 

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

x^4+2*x^3-3*x-6 = 0

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

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

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

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

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

( x+2 )

x+2 = 0 // - 2

x = -2

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -2} 

x = 2

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