Resposta:

[tex]\dfrac{2\sqrt{3} }{\sqrt{5} }=\dfrac{2\sqrt{3} .\sqrt{5} }{ \sqrt{5} .\sqrt{5} }=\dfrac{2\sqrt{3.5} }{\sqrt{25} }=\boxed{\dfrac{2\sqrt{15} }5}}[/tex]

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[tex]\dfrac{(\sqrt{2} -\sqrt{7} )(\sqrt{3} -1)}{(\sqrt{3}+1)(\sqrt{3} -1)}=\\ \\ \\ \dfrac{\sqrt{6} -\sqrt{2} -\sqrt{21} +\sqrt{7} }{(\sqrt{3}) ^2-1^2}=\\ \\ \\ \dfrac{\sqrt{6} -\sqrt{2} -\sqrt{21} +\sqrt{7} }{3-1}=\\ \\ \\\boxed{ \dfrac{\sqrt{6} -\sqrt{2} -\sqrt{21} +\sqrt{7} }{2}}[/tex]