((4x/9-x^2)-x-3/9+3x)×18(x-3)/x+3

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To simplify the expression, we can first combine like terms in the numerator:

(4x/9 - x^2 - x - 3/9 + 3x) = (4x/9 + 3x - x^2 - x - 3/9)
= (7x/9 - x^2 - 12/9)
= (7x/9 - x^2 - 4/3)
= (x(7/9 - x) - 4/3)

Now, we can multiply this simplified expression by 18(x - 3)/(x + 3):

[(x(7/9 - x) - 4/3)] * [18(x - 3)/(x + 3)]

= [18(x - 3)(7/9 - x) - 4/3(18)(x - 3)] / (x + 3)
= [18(x7/9 - x3 - 37/9 + 3x) - 4/318x - 4/3(-3)] / (x + 3)
= [18(7x/9 - 3x - 7/3 + 3x) - 72x + 43] / (x + 3)
= [18(7x/9 + 3x - 7/3) - 72x + 12] / (x + 3)
= [18(10x/9 - 7/3) - 72x + 12] / (x + 3)
= [20x - 42 - 72x + 12] / (x + 3)
= [-52x - 30] / (x + 3)

Therefore, the simplified expression is (-52x - 30) / (x + 3).