(x^4-12x^2)/(x^2-4)^2

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Solution for (x^4-12x^2)/(x^2-4)^2 equation: 


D( x )

(x^2-4)^2 = 0

(x^2-4)^2 = 0

(x^2-4)^2 = 0

1*x^2 = 4 // : 1

x^2 = 4

x^2 = 4 // ^ 1/2

abs(x) = 2

x = 2 or x = -2

x in (-oo:-2) U (-2:2) U (2:+oo)

(x^4-(12*x^2))/((x^2-4)^2) = 0

(x^4-12*x^2)/((x^2-4)^2) = 0

x^4-12*x^2 = 0

x^2*(x^2-12) = 0

1*x^2 = 12 // : 1

x^2 = 12

x^2 = 12 // ^ 1/2

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

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

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

(x^2*(x-2*3^(1/2))*(x+2*3^(1/2)))/((x^2-4)^2) = 0

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

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

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

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

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

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

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

x = 2*3^(1/2)

( x^2 )

1*x^2 = 0 // : 1

x^2 = 0

x = 0

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

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