((t^3-3t)/(t-t^4))*((t^4-t)/(3t-t^3))

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Solution for ((t^3-3t)/(t-t^4))*((t^4-t)/(3t-t^3)) equation:


D( t )

t-t^4 = 0

3*t-t^3 = 0

t-t^4 = 0

t-t^4 = 0

t-t^4 = 0

t*(1-t^3) = 0

-1*t^3 = -1 // : -1

t^3 = 1

t^3 = 1 // ^ 1/3

t = 1

t = 0

t = 0

3*t-t^3 = 0

3*t-t^3 = 0

3*t-t^3 = 0

t*(3-t^2) = 0

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

t^2 = 3

t^2 = 3 // ^ 1/2

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

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

t = 0

t = 0

t in (-oo:-3^(1/2)) U (-3^(1/2):0) U (0:1) U (1:3^(1/2)) U (3^(1/2):+oo)

((t^3-(3*t))/(t-t^4))*((t^4-t)/(3*t-t^3)) = 0

((t^3-3*t)/(t-t^4))*((t^4-t)/(3*t-t^3)) = 0

((t^3-3*t)*(t^4-t))/((t-t^4)*(3*t-t^3)) = 0

t^3-3*t = 0

t*(t^2-3) = 0

1*t^2 = 3 // : 1

t^2 = 3

t^2 = 3 // ^ 1/2

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

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

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

t-t^4 = 0

t*(1-t^3) = 0

-1*t^3 = -1 // : -1

t^3 = 1

t^3 = 1 // ^ 1/3

t = 1

t*(t-1) = 0

t^4-t = 0

t*(t^3-1) = 0

1*t^3 = 1 // : 1

t^3 = 1

t^3 = 1 // ^ 1/3

t = 1

t*(t-1) = 0

3*t-t^3 = 0

t*(3-t^2) = 0

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

t^2 = 3

t^2 = 3 // ^ 1/2

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

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

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

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

( t+3^(1/2) )

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

t = -3^(1/2)

( t-1 )

t-1 = 0 // + 1

t = 1

( t-3^(1/2) )

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

t = 3^(1/2)

( t )

t = 0

t in { -3^(1/2)}

t in { 1}

t in { 3^(1/2)}

t in { 0}

t belongs to the empty set

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