(1) 11+2+3=1+2−3(1+2)2−3=1+2−31+22+2−3=1+2−322=2+2−64=2+2−64\frac{1}{1+\sqrt{2}+\sqrt{3}} = \frac{1+\sqrt{2}-\sqrt{3}}{\left(1+\sqrt{2}\right)^2-3} = \frac{1+\sqrt{2}-\sqrt{3}}{1+2\sqrt{2}+2-3} = \frac{1+\sqrt{2}-\sqrt{3}}{2\sqrt{2}} = \frac{\sqrt{2}+2-\sqrt{6}}{4} = \frac{2+\sqrt{2}-\sqrt{6}}{4}1+2+31=(1+2)2−31+2−3=1+22+2−31+2−3=221+2−3=42+2−6=42+2−6 (2) 12+3+5=2+3−5(2+3)2−5=2+3−52+26+3−5=2+3−526=23+32−3012\frac{1}{\sqrt{2}+\sqrt{3}+\sqrt{5}} = \frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{\left(\sqrt{2}+\sqrt{3}\right)^2-5} = \frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{2+2\sqrt{6}+3-5} = \frac{\sqrt{2}+\sqrt{3}-\sqrt{5}}{2\sqrt{6}} = \frac{2\sqrt{3}+3\sqrt{2}-\sqrt{30}}{12}2+3+51=(2+3)2−52+3−5=2+26+3−52+3−5=262+3−5=1223+32−30