((x^4)-27x^2)/(x^2-9)^2

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Solution for ((x^4)-27x^2)/(x^2-9)^2 equation: 


D( x )

(x^2-9)^2 = 0

(x^2-9)^2 = 0

(x^2-9)^2 = 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 (-3:3) U (3:+oo)

(x^4-(27*x^2))/((x^2-9)^2) = 0

(x^4-27*x^2)/((x^2-9)^2) = 0

x^4-27*x^2 = 0

x^2*(x^2-27) = 0

1*x^2 = 27 // : 1

x^2 = 27

x^2 = 27 // ^ 1/2

abs(x) = 3*3^(1/2)

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

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

(x^2*(x-3*3^(1/2))*(x+3*3^(1/2)))/((x^2-9)^2) = 0

( x+3*3^(1/2) )

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

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

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

( x-3*3^(1/2) )

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

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

x = 3*3^(1/2)

( x^2 )

1*x^2 = 0 // : 1

x^2 = 0

x = 0

x in { -3*3^(1/2), 3*3^(1/2), 0 }

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