[tex]~~~\dfrac{2\sqrt 2 + \sqrt 7}{2\sqrt 2 -\sqrt 7} + \dfrac{2\sqrt 2-\sqrt 7 }{2\sqrt 2+\sqrt 7}\\\\\\=\dfrac{\sqrt 8 + \sqrt 7}{\sqrt 8 -\sqrt 7} + \dfrac{\sqrt 8-\sqrt 7 }{\sqrt 8+\sqrt 7}\\\\\\=\dfrac{\left(\sqrt 8 +\sqrt 7\right)^2+\left(\sqrt 8 -\sqrt 7\right)^2 }{\left(\sqrt 8 -\sqrt 7\right)\left(\sqrt 8 +\sqrt 7\right)}\\\\\\[/tex]
[tex]=\dfrac{\left(\sqrt 8+ \sqrt 7 + \sqrt 8 - \sqrt 7 \right)^2 - 2 \left(\sqrt 8 +\sqrt 7\right)\left(\sqrt 8 -\sqrt 7\right)}{\left(\sqrt 8 \right)^2 - \left(\sqrt 7 \right)^2}\\\\\\=\dfrac{\left(2\sqrt 8 \right)^2 - 2(8-7)}{8-7}\\\\\\=\dfrac{4 \cdot 8 -2\cdot 1}{1}\\\\\\=32 -2 \\\\\\=30[/tex]
