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Determine all of the asymptotes of the function:

$$f(x)=\cfrac{x+2}{{x}^{2}+6x+8}$$

A

$x=-2$, $x=-4$, $y=0$

B

$y=-2$, $x=-2$, $x=-4$

C

$x=-4$, $y=0$

D

$x=-2$, $y=0$

E

$x=0$, $y=-2$

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