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D( x )
x^3-(4*x^2)+3*x = 0
x^3-(4*x^2)+3*x = 0
x^3-(4*x^2)+3*x = 0
x^3-4*x^2+3*x = 0
x^3-4*x^2+3*x = 0
x*(x^2-4*x+3) = 0
x^2-4*x+3 = 0
DELTA = (-4)^2-(1*3*4)
DELTA = 4
DELTA > 0
x = (4^(1/2)+4)/(1*2) or x = (4-4^(1/2))/(1*2)
x = 3 or x = 1
x = 0
x = 0
x in (-oo:0) U (0:1) U (1:3) U (3:+oo)
(12*x-4*x^2)/(x^3-(4*x^2)+3*x) = 0
(12*x-4*x^2)/(x^3-4*x^2+3*x) = 0
12*x-4*x^2 = 0
4*x*(3-x) = 0
3-x = 0 // - 3
-x = -3 // * -1
x = 3
4*x*(x-3) = 0
x^3-4*x^2+3*x = 0
x*(x^2-4*x+3) = 0
x^2-4*x+3 = 0
DELTA = (-4)^2-(1*3*4)
DELTA = 4
DELTA > 0
x = (4^(1/2)+4)/(1*2) or x = (4-4^(1/2))/(1*2)
x = 3 or x = 1
x*(x-1)*(x-3) = 0
(4*x*(x-3))/(x*(x-1)*(x-3)) = 0
( 4*x )
4*x = 0 // : 4
x = 0
( x-3 )
x-3 = 0 // + 3
x = 3
x in { 0}
x in { 3}
x belongs to the empty set
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