a) [tex]\frac{4}{-1 + \sqrt{6} } * \frac{-1-\sqrt{6} }{-1-\sqrt{6} } = \frac{4(-1-\sqrt{6}) }{(-1+\sqrt{6})(-1-\sqrt{6} ) } = \frac{-4-4\sqrt{6} }{(1- 6)} = \frac{-4-4\sqrt{6} }{-5}[/tex]
b) [tex]\frac{\sqrt{3} }{\sqrt{2} } + 5 = \frac{(\sqrt{3})(\sqrt{2}) }{(\sqrt{3})(\sqrt{3}) } + 5 = \frac{\sqrt{6} }{3} + 5 = \frac{\sqrt{6} }{3} + \frac{15}{3} = \frac{15+\sqrt{6} }{3}[/tex]
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a) [tex]\frac{4}{-1 + \sqrt{6} } * \frac{-1-\sqrt{6} }{-1-\sqrt{6} } = \frac{4(-1-\sqrt{6}) }{(-1+\sqrt{6})(-1-\sqrt{6} ) } = \frac{-4-4\sqrt{6} }{(1- 6)} = \frac{-4-4\sqrt{6} }{-5}[/tex]
b) [tex]\frac{\sqrt{3} }{\sqrt{2} } + 5 = \frac{(\sqrt{3})(\sqrt{2}) }{(\sqrt{3})(\sqrt{3}) } + 5 = \frac{\sqrt{6} }{3} + 5 = \frac{\sqrt{6} }{3} + \frac{15}{3} = \frac{15+\sqrt{6} }{3}[/tex]