${4 \over {1 + \sqrt 2 - \sqrt 3 }} = $
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a
(a) \({4 \over {1 + \sqrt 2 - \sqrt 3 }} = {{4\,(1 + \sqrt 2 + \sqrt 3 )} \over {{{(1 + \sqrt 2 )}^2} - 3}}\)
(a) \({4 \over {1 + \sqrt 2 - \sqrt 3 }} = {{4\,(1 + \sqrt 2 + \sqrt 3 )} \over {{{(1 + \sqrt 2 )}^2} - 3}}\)
\( = {{4(1 + \sqrt 2 + \sqrt 3 )} \over {3 + 2\sqrt 2 - 3}} + {{\sqrt 6 (\sqrt 3 - \sqrt 2 )} \over {3 - 2}}\)
\( = \sqrt 2 (1 + \sqrt 2 + \sqrt 3 ) = 2 + \sqrt 2 + \sqrt 6 \).
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