Question

$\frac{2}{ \sqrt{11} - \sqrt{10} } + \frac{4}{\sqrt{11} + \sqrt{10}}$
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Answer 1

$\frac{2}{ \sqrt{11} - \sqrt{10} } + \frac{4}{ \sqrt{11} + \sqrt{10} }= \frac{2(\sqrt{11} + \sqrt{10})+4(\sqrt{11} - \sqrt{10})}{(\sqrt{11} - \sqrt{10})(\sqrt{11} + \sqrt{10})} =$

$=\frac{2\sqrt{11} + 2\sqrt{10}+4\sqrt{11} - 4\sqrt{10}}{(\sqrt{11})^2 - (\sqrt{10})^2} =\frac{6\sqrt{11} - 2\sqrt{10} }{11 - 10} =6\sqrt{11} - 2\sqrt{10}$