[tex]\dfrac{\sqrt 2 + \sqrt 3}{\sqrt 2 - \sqrt 3} + \dfrac{\sqrt 2 - \sqrt 3}{\sqrt 2 + \sqrt 3}\\\\\\=\dfrac{\left( \sqrt 2+\sqrt 3\right)^2 + \left( \sqrt 2-\sqrt 3\right)^2}{\left( \sqrt 2-\sqrt 3\right)\left( \sqrt 2+\sqrt 3\right)}\\\\\\[/tex]
[tex]=\dfrac{\left( \sqrt 2 + \sqrt 3+ \sqrt 2-\sqrt 3\right)^2 - 2\left( \sqrt 2+\sqrt 3\right)\left( \sqrt 2-\sqrt 3\right)}{\left(\sqrt 2\right)^2 - \left(\sqrt 3 \right)^2}\\\\\\=\dfrac{\left(2\sqrt 2 \right)^2 -2 (2-3)}{2-3}\\\\\\=\dfrac{8-2(-1)}{-1}\\\\\\=-(8+2)\\\\\\=-10[/tex]
