Proof- division. Is it a true statement or false

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Prove that $\forall a,b,c,d$ E Z, if $a | c$ and $b | d$ then $(a+b) | (c+d)$

I've got up to here

$$c=ax$$ $$d=by$$ So $$c+d = ax+by$$

I believe that this a false statement but I don’t know where to go from here