Answer
$\displaystyle \frac{x}{x+3}$
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.
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Numerator $:$ factor out x...
$x(x^{2}-3x+9)=$
... and, this is as far as it goes
(not a perfect square, can't find factors of 9 whose sum is -3)
Denominator:
Numerator $:$ recognize a sum of cubes
$x^{3}+3^{3}=(x+3)(x^{2}-3x+9)$
Expression = $\displaystyle \frac{x(x^{2}-3x+9)}{(x+3)(x^{2}-3x+9)}$
... divide both with the common factor: $(x^{2}-3x+9)$
Expression = $\displaystyle \frac{x}{x+3}$
