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2) $B=\frac{\sqrt{2}}{1+\sqrt{2}-\sqrt{3}}=\frac{\sqrt{2}(1-\sqrt{2}+\sqrt{3})}{(1+\sqrt{2}-\sqrt{3})(1-\sqrt{2}+\sqrt{3})}$
$=\frac{\sqrt{2}(1-\sqrt{2}-\sqrt{3})}{1-(\sqrt{2}-\sqrt{3})^2}=\frac{\sqrt{2}(1-\sqrt{2}-\sqrt{3})}{2\sqrt 6-4}=\frac{\sqrt{2}(1-\sqrt{2}-\sqrt{3})(2\sqrt 6+4)}{(2\sqrt 6-4)(2\sqrt 6+4)}$
$=\frac{\sqrt{2}(1-\sqrt{2}-\sqrt{3})(2\sqrt 6+4)}{24-16}=\frac{\sqrt{2}(1-\sqrt{2}-\sqrt{3})(2\sqrt 6+4)}{8}$
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