[tex]\frac{1}{\sqrt{12}+\sqrt{2} } =\frac{1}{2\sqrt{3}+\sqrt{2} } *\frac{\sqrt{2} }{\sqrt{2} } =\frac{\sqrt{2} }{2\sqrt{6} } *\frac{\sqrt{6} }{\sqrt{6} } =\frac{\sqrt{12} }{2\sqrt{36} } =\frac{2\sqrt{3} }{12}[/tex]
[tex]\frac{\sqrt{17}-\sqrt{3} }{\sqrt{10} } *\frac{\sqrt{10} }{\sqrt{10} } =\frac{\sqrt{170}-\sqrt{30} }{\sqrt{100} } =\frac{\sqrt{170} -\sqrt{30} }{10}[/tex]
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[tex]\frac{1}{\sqrt{12}+\sqrt{2} } =\frac{1}{2\sqrt{3}+\sqrt{2} } *\frac{\sqrt{2} }{\sqrt{2} } =\frac{\sqrt{2} }{2\sqrt{6} } *\frac{\sqrt{6} }{\sqrt{6} } =\frac{\sqrt{12} }{2\sqrt{36} } =\frac{2\sqrt{3} }{12}[/tex]
[tex]\frac{\sqrt{17}-\sqrt{3} }{\sqrt{10} } *\frac{\sqrt{10} }{\sqrt{10} } =\frac{\sqrt{170}-\sqrt{30} }{\sqrt{100} } =\frac{\sqrt{170} -\sqrt{30} }{10}[/tex]