(72-8x^2+4x^3-36x)/(x-3)

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Solution for (72-8x^2+4x^3-36x)/(x-3) equation: 


D( x )

x-3 = 0

x-3 = 0

x-3 = 0

x-3 = 0 // + 3

x = 3

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

(4*x^3-(8*x^2)-(36*x)+72)/(x-3) = 0

(4*x^3-8*x^2-36*x+72)/(x-3) = 0

4*x^3-8*x^2-36*x+72 = 0

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

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

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

1

x = 1

x^3-2*x^2-9*x+18 = 8

1

-1

x = -1

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

-1

2

x = 2

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

2

x-2

x^2-9

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

x-2

2*x^2-x^3

18-9*x

9*x-18

0

x^2-9 = 0

DELTA = 0^2-(-9*1*4)

DELTA = 36

DELTA > 0

x = (36^(1/2)+0)/(1*2) or x = (0-36^(1/2))/(1*2)

x = 3 or x = -3

x in { -3, 3, 2} 

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

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

( x+3 )

x+3 = 0 // - 3

x = -3

( x-2 )

x-2 = 0 // + 2

x = 2

x in { -3, 2 }

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