Answer
$\displaystyle \frac{x^{2}+2x+4}{x+4}$
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:
search for integer factors of $-8$ whose sum is $+2$...
... these are $+4$ and $-2...$
$x^{2}+2x-8 =(x+4)(x-2)$
Expression = $\displaystyle \frac{(x-2)(x^{2}+2x+4)}{(x+4)(x-2)}$
... divide both with the common factor: $ (x-2)$
Expression = $\displaystyle \frac{x^{2}+2x+4}{x+4}$
