(6m-4/m^3)/(3m-2/m)

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Solution for (6m-4/m^3)/(3m-2/m) equation:


D( m )

3*m-(2/m) = 0

m = 0

m^3 = 0

3*m-(2/m) = 0

3*m-(2/m) = 0

3*m-2*m^-1 = 0

3*m^1-2*m^-1 = 0

(3*m^2-2*m^0)/(m^1) = 0 // * m^2

m^1*(3*m^2-2*m^0) = 0

m^1

3*m^2-2 = 0

3*m^2-2 = 0

DELTA = 0^2-(-2*3*4)

DELTA = 24

DELTA > 0

m = (24^(1/2)+0)/(2*3) or m = (0-24^(1/2))/(2*3)

m = (1*6^(1/2))/3 or m = (-6^(1/2))/3

m in { (-6^(1/2))/3, (1*6^(1/2))/3}

m = 0

m = 0

m^3 = 0

m^3 = 0

1*m^3 = 0 // : 1

m^3 = 0

m = 0

m in (-oo:(-6^(1/2))/3) U ((-6^(1/2))/3:0) U (0:(1*6^(1/2))/3) U ((1*6^(1/2))/3:+oo)

(6*m-(4/(m^3)))/(3*m-(2/m)) = 0

(6*m-4*m^-3)/(3*m-2*m^-1) = 0

6*m-4*m^-3 = 0

2*m*(3-2*m^-4) = 0

-2*m^-4 = -3 // : -2

m^-4 = 3/2

-4 < 0

1/(m^4) = 3/2 // * m^4

1 = 3/2*m^4 // : 3/2

2/3 = m^4

m^4 = 2/3 // ^ 1/4

abs(m) = (2/3)^(1/4)

m = (2/3)^(1/4) or m = -(2/3)^(1/4)

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

3*m-2*m^-1 = 0

m^-1*(3*m^2-2) = 0

3*m^2 = 2 // : 3

m^2 = 2/3

m^2 = 2/3 // ^ 1/2

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

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

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

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

( 2*m )

2*m = 0 // : 2

m = 0

( m+(2/3)^(1/4) )

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

m = -(2/3)^(1/4)

( m-(2/3)^(1/4) )

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

m = (2/3)^(1/4)

m in { 0}

m in { -(2/3)^(1/4), (2/3)^(1/4) }

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