\(\left(2\sqrt{3+\sqrt{5-\sqrt{13+\sqrt{48}}}}\right):\left(\sqrt{6}+\sqrt{2}\right)\)
=\(\left(2\sqrt{3+\sqrt{5-\sqrt{13+2\sqrt{12}}}}\right):\left(\sqrt{6}+\sqrt{2}\right)\)
= \(\left(2\sqrt{3+\sqrt{5-\left|\sqrt{12}+1\right|}}\right):\left(\sqrt{6}+\sqrt{2}\right)\)
=\(\left(2\sqrt{3+\sqrt{5-\sqrt{12}-1}}\right):\left(\sqrt{6}+\sqrt{2}\right)\)
=\(\left(2\sqrt{3+\sqrt{4-2\sqrt{3}}}\right):\left(\sqrt{6}+\sqrt{2}\right)\)
= \(\left(2\sqrt{3+\left|\sqrt{3}-1\right|}\right):\left(\sqrt{6}+\sqrt{2}\right)\)
= \(\left(2\sqrt{3+\sqrt{3}-1}\right):\sqrt{2}\left(\sqrt{3}+1\right)\)
= \(\left(2\sqrt{2-\sqrt{3}}\right):\sqrt{2}\left(\sqrt{3}+1\right)\)
=\(\left(2.\frac{\left|1-\sqrt{3}\right|}{\sqrt{2}}\right):\sqrt{2}\left(\sqrt{3}+1\right)\)
= \(\sqrt{2}\left(\sqrt{3}+1\right):\sqrt{2}\left(\sqrt{3}+1\right)\)
= \(1\)
