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$B = \left ( 2+\sqrt 2 \right )\left (\frac{\sqrt 3 - \sqrt 2}{(\sqrt 3 - \sqrt 2)(\sqrt 3 + \sqrt 2)} +\frac{2-\sqrt 3}{(2-\sqrt 3)(2+\sqrt 3)}\right )$
$B = \left ( 2+\sqrt 2 \right )\left (\sqrt 3 - \sqrt 2 +2-\sqrt 3\right )$
$B = \left ( 2+\sqrt 2 \right )\left (2 - \sqrt 2 \right )$
$B=4-2=2.$
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