A1. What do we get after rationalizing the expression $\frac{4+2 \sqrt{6}}{(1+\sqrt{2})+\sqrt{3}}$?
(A) $1-\sqrt{2}-\sqrt{3}$
(B) $1-\sqrt{2}+\sqrt{3}$
(C) $1+\sqrt{2}+\sqrt{3}$
(D) $-1+\sqrt{2}+\sqrt{3}$
(E) $-1+\sqrt{2}-\sqrt{3}$