Answer
$x^{2}+2x+4$
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: recognize a difference of cubes:
$x^{3}-2^{3}=(x-2)(x^{2}+2x+4)$
Denominator: fully factored.
Expression = $\displaystyle \frac{(x-2)(x^{2}+2x+4)}{(x-2)}$
... divide both with the common factor: $(x+4)$
Expression = $\displaystyle \frac{x^{2}+2x+4}{1}$ = $x^{2}+2x+4$