[tex]\frac{2(\sqrt{5}+1)}{\sqrt{10}-\sqrt{2}}=\frac{2(\sqrt{5}+1)(\sqrt{10}+\sqrt{2})}{(\sqrt{10}-\sqrt{2})(\sqrt{10}+\sqrt{2})} =\frac{2(\sqrt{50}+\sqrt{10}+\sqrt{10}+\sqrt{2} )}{10-2}= \frac{2(5\sqrt{2}+2\sqrt{10}+\sqrt{2}) }{8} =\frac{5\sqrt{2}+2\sqrt{10}+\sqrt{2} }{4}[/tex]