(6x^3-4x)/x

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Solution for (6x^3-4x)/x equation:


D( x )

x = 0

x = 0

x = 0

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

(6*x^3-(4*x))/x = 0

(6*x^3-4*x)/x = 0

6*x^3-4*x = 0

2*x*(3*x^2-2) = 0

3*x^2 = 2 // : 3

x^2 = 2/3

x^2 = 2/3 // ^ 1/2

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

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

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

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

( 2*x )

2*x = 0 // : 2

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

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

x in { 0}

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

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