((X^2-x-2)/(x^3+6x^2-x-30))*((x+3)/(x+1))

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Solution for ((X^2-x-2)/(x^3+6x^2-x-30))*((x+3)/(x+1)) equation: 


D( x )

x^3+6*x^2-x-30 = 0

x+1 = 0

x^3+6*x^2-x-30 = 0

x^3+6*x^2-x-30 = 0

x^3+6*x^2-x-30 = 0

{ 1, -1, 2, -2, 3, -3, 5, -5, 6, -6, 10, -10, 15, -15, 30, -30 }

1

x = 1

x^3+6*x^2-x-30 = -24

1

-1

x = -1

x^3+6*x^2-x-30 = -24

-1

2

x = 2

x^3+6*x^2-x-30 = 0

2

x-2

x^2+8*x+15

x^3+6*x^2-x-30

x-2

2*x^2-x^3

8*x^2-x-30

16*x-8*x^2

15*x-30

30-15*x

0

x^2+8*x+15 = 0

DELTA = 8^2-(1*4*15)

DELTA = 4

DELTA > 0

x = (4^(1/2)-8)/(1*2) or x = (-4^(1/2)-8)/(1*2)

x = -3 or x = -5

x in { -5, -3, 2} 

x+1 = 0

x+1 = 0

x+1 = 0 // - 1

x = -1

x in (-oo:-5) U (-5:-3) U (-3:-1) U (-1:2) U (2:+oo)

((X^2-x-2)/(x^3+6*x^2-x-30))*((x+3)/(x+1)) = 0

((X^2-x-2)*(x+3))/((x^3+6*x^2-x-30)*(x+1)) = 0

x^3+6*x^2-x-30 = 0

x^3+6*x^2-x-30 = 0

{ 1, -1, 2, -2, 3, -3, 5, -5, 6, -6, 10, -10, 15, -15, 30, -30 }

1

x = 1

x^3+6*x^2-x-30 = -24

1

-1

x = -1

x^3+6*x^2-x-30 = -24

-1

2

x = 2

x^3+6*x^2-x-30 = 0

2

x-2

x^2+8*x+15

x^3+6*x^2-x-30

x-2

2*x^2-x^3

8*x^2-x-30

16*x-8*x^2

15*x-30

30-15*x

0

x^2+8*x+15 = 0

DELTA = 8^2-(1*4*15)

DELTA = 4

DELTA > 0

x = (4^(1/2)-8)/(1*2) or x = (-4^(1/2)-8)/(1*2)

x = -3 or x = -5

x in { -5, -3, 2} 

(x+5)*(x+3)*(x-2) = 0

(X^2-x-2)/((x+5)*(x-2)*(x+1)) = 0

X^2-x-2 = 0 // - X^2-2

-x = -(X^2-2) // * -1

x = X^2-2

x = X^2-2

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