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Which one of the following is equivalent to $\cfrac{{(x}^{2}-{y}^{2})}{2(x+y)+(x+y)}(x>0,y>0)$?

$(x-y)$

$\cfrac{x+y}{3}$

$\cfrac{x-y}{3}$

$\cfrac{x-y}{x+y}$

$(x+y)$