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.
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.