(x^5+5x^3-6x)/(x-1)

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Solution for (x^5+5x^3-6x)/(x-1) equation:


D( x )

x-1 = 0

x-1 = 0

x-1 = 0

x-1 = 0 // + 1

x = 1

x in (-oo:1) U (1:+oo)

(x^5+5*x^3-(6*x))/(x-1) = 0

(x^5+5*x^3-6*x)/(x-1) = 0

x^5+5*x^3-6*x = 0

x*(x^4+5*x^2-6) = 0

x^4+5*x^2-6 = 0

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

1

x = 1

x^4+5*x^2-6 = 0

1

x-1

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

x^4+5*x^2-6

x-1

x^3-x^4

x^3+5*x^2-6

x^2-x^3

6*x^2-6

6*x-6*x^2

6*x-6

6-6*x

0

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

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

1

x = 1

x^3+x^2+6*x+6 = 14

1

-1

x = -1

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

-1

x+1

x^2+6

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

x+1

-x^3-x^2

6*x+6

-6*x-6

0

x^2+6 = 0

DELTA = 0^2-(1*4*6)

DELTA = -24

DELTA < 0

x in { 1, -1}

x*(x-1)*(x+1) = 0

x*(x+1) = 0

( x+1 )

x+1 = 0 // - 1

x = -1

( x )

x = 0

x in { -1, 0 }

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