(5x^4+14x^3+9x)/(x^2+3x)

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Solution for (5x^4+14x^3+9x)/(x^2+3x) equation:


D( x )

x^2+3*x = 0

x^2+3*x = 0

x^2+3*x = 0

x^2+3*x = 0

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

DELTA = 9

DELTA > 0

x = (9^(1/2)-3)/(1*2) or x = (-9^(1/2)-3)/(1*2)

x = 0 or x = -3

x in (-oo:-3) U (-3:0) U (0:+oo)

(5*x^4+14*x^3+9*x)/(x^2+3*x) = 0

5*x^4+14*x^3+9*x = 0

x*(5*x^3+14*x^2+9) = 0

5*x^3+14*x^2+9 = 0

{ 1, -1, 3, -3, 9, -9 }

1

x = 1

5*x^3+14*x^2+9 = 28

1

-1

x = -1

5*x^3+14*x^2+9 = 18

-1

3

x = 3

5*x^3+14*x^2+9 = 270

3

-3

x = -3

5*x^3+14*x^2+9 = 0

-3

x+3

5*x^2-x+3

5*x^3+14*x^2+9

x+3

-5*x^3-15*x^2

9-x^2

x^2+3*x

3*x+9

-3*x-9

0

5*x^2-x+3 = 0

DELTA = (-1)^2-(3*4*5)

DELTA = -59

DELTA < 0

x in { -3}

x*(x+3) = 0

x^2+3*x = 0

x*(x+3) = 0

x+3 = 0 // - 3

x = -3

x*(x+3) = 0

(x*(x+3))/(x*(x+3)) = 0

( x+3 )

x+3 = 0 // - 3

x = -3

( x )

x = 0

x in { -3}

x in { 0}

x belongs to the empty set

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