Explanation:
We can use polynomial long division to simplify the expression:
x^2 + 3x + 15
------------------
x - 3 | x^3 - 3x^2 + 6x - 18
- (x^3 - 3x^2 + 9x)
--------------------
-3x - 18
- (-3x + 9)
----------
-9
Therefore,
(x^3 - 3x^2 + 6x - 18) / (x - 3) = x^2 + 3x + 15 - 9/(x-3)
So the simplified expression is x^2 + 3x + 15 - 9/(x-3).