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x/6 - 2x/3 + 2/9 = 0 lo multiplicamos por 6 y 3
(x*3*6)/6 - (2x*3*6)/3 + 2(6*3)/9 = 0*6*3
3x-12x+36/9=0
3x-12x+4=0
-9x=-4
x=4/9 la respuesta a tu problema
x*(1/6-2/3) + 2/9 = 0
x*(1/6-4/6) + 2/9 = 0
-3x/6 + 2/9 = 0
-3x/6 = -2/9
x = (-2/9) * (6/-3) = -12/-27 = 4/9
Respuesta:
x = 4/9