9a-a^3⁄a-3+3a^2-27⁄a+3-(a^2-9)

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To simplify this expression, we can first rewrite it as:

9a - (a^3/(a-3)) + (3a^2 - 27)/(a+3) - (a^2 - 9)

Next, we can factor the numerator of the fraction in the second term:

a^3 = a^2 * a

Substitute this into the expression:

9a - (a^2 * (a/(a-3))) + (3a^2 - 27)/(a+3) - (a^2 - 9)

Now, we can factor out a common factor of 3 from the numerator of the second fraction:

(3(a^2 - 9))/(a+3)

Now, factor the numerator as the difference of squares:

(3(a + 3)(a - 3))/(a + 3)

Simplify by canceling out the common factor of (a + 3):

3(a - 3)

Now, substitute this back into the expression:

9a - (a^2 * (a/(a-3))) + (3a^2 - 3(a - 3)) - (a^2 - 9)

Further simplifying:

9a - a^2 * (a/(a-3)) + 3a^2 - 3a + 9 - a^2 + 9

Combining like terms:

11a + 12

Therefore, the simplified expression is 11a + 12.