Answer
$\displaystyle \frac{x-6}{x^{2}+3x+9} $
Work Step by Step
Simplifying Rational Expressions
1. Factor the numerator and the denominator completely.
2. Divide both the numerator and the denominator by any common factors.
---
Numerator $:$ search for integer factors of $+18$ whose sum is $-9$...
... these are $-3$ and $-6...$
$x^{2}-9x+18 =(x-3)(x-6)$
Denominator:
recognize a difference of cubes
$x^{3}-3^{3}=(x-3)(x^{2}+3x+9)$
Expression = $\displaystyle \frac{(x-3)(x-6)}{(x-3)(x^{2}+3x+9)}$
... divide both with the common factor: $ (x-3)$
Expression = $\displaystyle \frac{x-6}{x^{2}+3x+9} $
