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D( x )
9*x^2-(6*x) = 0
9*x^2-(6*x) = 0
9*x^2-(6*x) = 0
9*x^2-6*x = 0
9*x^2-6*x = 0
DELTA = (-6)^2-(0*4*9)
DELTA = 36
DELTA > 0
x = (36^(1/2)+6)/(2*9) or x = (6-36^(1/2))/(2*9)
x = 2/3 or x = 0
x in (-oo:0) U (0:2/3) U (2/3:+oo)
x/(9*x^2-(6*x)) > 0
x/(9*x^2-6*x) > 0
9*x^2-6*x = 0
3*x*(3*x-2) = 0
3*x-2 = 0 // + 2
3*x = 2 // : 3
x = 2/3
3*x*(x-2/3) = 0
x/(3*x*(x-2/3)) > 0
( 3*x )
3*x+0 > 0 // - 0
3*x > 0 // : 3
x > 0/3
x > 0
( x-2/3 )
x-2/3 > 0 // + 2/3
x > 2/3
( x )
x+0 > 0 // - 0
x > 0
(-oo:0) (0:2/3) (2/3:+oo) 3*x - + + x-2/3 - - + x - + +
x in (2/3:+oo)
(2/3:+oo)
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