(3x^6/(x^2-9))*((x^2+6x+9)/(9x^7))

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Solution for (3x^6/(x^2-9))*((x^2+6x+9)/(9x^7)) equation: 


D( x )

9*x^7 = 0

x^2-9 = 0

9*x^7 = 0

9*x^7 = 0

9*x^7 = 0 // : 9

x^7 = 0

x = 0

x^2-9 = 0

x^2-9 = 0

1*x^2 = 9 // : 1

x^2 = 9

x^2 = 9 // ^ 1/2

abs(x) = 3

x = 3 or x = -3

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

((3*x^6)/(x^2-9))*((x^2+6*x+9)/(9*x^7)) = 0

(3*x^6*(x^2+6*x+9))/(9*x^7*(x^2-9)) = 0

x^2+6*x+9 = 0

x^2+6*x+9 = 0

DELTA = 6^2-(1*4*9)

DELTA = 0

x = -6/(1*2)

x = -3 or x = -3

(x+3)^2 = 0

(3*x^6*(x+3)^2)/(9*x^7*(x^2-9)) = 0

( 3*x^6 )

3*x^6 = 0 // : 3

x^6 = 0

x = 0

( x+3 )

x+3 = 0 // - 3

x = -3

x in { 0} 

x in { -3} 

x belongs to the empty set

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