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Which one of the following is equivalent to $\cfrac{{a}^{2}+6a+9}{2a+6}(a\neq-3)$ ?

A

$a+3$

B

$a-3$

C

$\cfrac{a+3}{2}$

D

$\cfrac{a-3}{2}$

E

$\cfrac{{(a+3})^{2}}{2}$

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