\(\dfrac{\sqrt{8-2\sqrt{15}}}{\sqrt{10}-\sqrt{6}}=\dfrac{\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}}{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}=\dfrac{1}{\sqrt{2}}\)
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\(\dfrac{\sqrt{8-2\sqrt{15}}}{\sqrt{10}-\sqrt{6}}\)
=\(\dfrac{\sqrt{\left(\sqrt{5}-\sqrt{3}\right)^2}}{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}\)
=\(\dfrac{\sqrt{5}-\sqrt{3}}{\sqrt{2}\left(\sqrt{5}-\sqrt{3}\right)}\)
=\(\dfrac{1}{\sqrt{2}}\)
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