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[tex]\frac{\sqrt{7} - \sqrt{3} }{\sqrt{21} } =\frac{\sqrt{7*}\sqrt{21} - \sqrt{3} *\sqrt{21} }{\sqrt{21}*\sqrt{21} }=\frac{\sqrt{141}+ \sqrt{63} }{21}[/tex]
[tex]\frac{\sqrt{2} +\sqrt{5} }{\sqrt{10} } = \frac{\sqrt{2 }* \sqrt{10} +\sqrt{5}*\sqrt{10} }{\sqrt{10}*\sqrt{10} } =\frac{\sqrt{20}+\sqrt{50} }{10}[/tex]
[tex]\frac{\sqrt{5}-\sqrt{3} }{\sqrt{15} } =\frac{\sqrt{5}*\sqrt{15} -\sqrt{3} *\sqrt{15} }{\sqrt{15} *\sqrt{15} } =\frac{\sqrt{75}-\sqrt{45} }{15}[/tex] [tex]\frac{4\sqrt{2}-\sqrt{5} }{3\sqrt{10} } =\frac{4\sqrt{2} *\sqrt{10} -\sqrt{5} *\sqrt{10} }{3\sqrt{10} *\sqrt{10} } =\frac{4\sqrt{20}-\sqrt{50} }{30}[/tex] [tex]\frac{\sqrt{5} +2\sqrt{3} }{4\sqrt{15} } =\frac{\sqrt{5} *\sqrt{15} +2\sqrt{3}*\sqrt{15} }{4\sqrt{15}*\sqrt{15} } =\frac{\sqrt{75} +2\sqrt{45} }{60}[/tex] [tex]\frac{5\sqrt{2}-\sqrt{7} }{2\sqrt{14} } =\frac{5\sqrt{2} *\sqrt{14} -\sqrt{7}*\sqrt{14} }{2\sqrt{14}*\sqrt{14} } =\frac{5\sqrt{28} -\sqrt{98} }{28}[/tex]
