3x^2-6x/x^3-2x^2

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Solution for 3x^2-6x/x^3-2x^2 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^2-(2*x^2)-((6*x)/(x^3)) = 0

3*x^2-2*x^2-6*x^-2 = 0

x^2-6*x^-2 = 0

t_1 = x^2

1*t_1^1-6*t_1^-1 = 0

1*t_1^1-6*t_1^-1 = 0

(1*t_1^2-6*t_1^0)/(t_1^1) = 0 // * t_1^2

t_1^1*(1*t_1^2-6*t_1^0) = 0

t_1^1

t_1^2-6 = 0

t_1^2-6 = 0

DELTA = 0^2-(-6*1*4)

DELTA = 24

DELTA > 0

t_1 = (24^(1/2)+0)/(1*2) or t_1 = (0-24^(1/2))/(1*2)

t_1 = 6^(1/2) or t_1 = -6^(1/2)

t_1 in { -6^(1/2), 6^(1/2)} 

t_1 = -6^(1/2)

x^2+6^(1/2) = 0

1*x^2 = -6^(1/2) // : 1

x^2 = -6^(1/2)

t_1 = 6^(1/2)

x^2-6^(1/2) = 0

1*x^2 = 6^(1/2) // : 1

x^2 = 6^(1/2)

x^2 = 6^(1/2) // ^ 1/2

abs(x) = 6^(1/4)

x = 6^(1/4) or x = -6^(1/4)

x in { 6^(1/4), -6^(1/4) }

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