(3x-x^3)/x^3

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Solution for (3x-x^3)/x^3 equation: 


D( x )

x^3 = 0

x^3 = 0

x^3 = 0

1*x^3 = 0 // : 1

x^3 = 0

x = 0

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

(3*x-x^3)/(x^3) = 0

3*x-x^3 = 0

x*(3-x^2) = 0

-1*x^2 = -3 // : -1

x^2 = 3

x^2 = 3 // ^ 1/2

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

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

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

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

( x+3^(1/2) )

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

x = -3^(1/2)

( x-3^(1/2) )

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

x = 3^(1/2)

( x )

x = 0

x in { 0} 

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

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