=\(\frac{1}{\sqrt{7-2\sqrt{6}_{ }}+1}+\frac{1}{\sqrt{7+2\sqrt{6}}+1}\)
=\(\frac{1}{\sqrt{\left(\sqrt{6}-1\right)^2+1}}+\frac{1}{\sqrt{\left(\sqrt{6+1}\right)^2}+1}\)
=\(\frac{1}{\sqrt{6}}+\frac{1}{\sqrt{6}+2}\)
=\(\frac{\sqrt{6}+2+\sqrt{6}}{\sqrt{6}\left(\sqrt{6}+2\right)}\)
=\(\frac{2\sqrt{6}+2}{6+2\sqrt{6}}\)