$$\frac{\sqrt{2}+\sqrt{7}}{\sqrt{8}+\sqrt{7}}\\\\
=\frac{(\sqrt{2}+\sqrt{7})(\sqrt{8}-\sqrt{7})}{(\sqrt{8}+\sqrt{7})(\sqrt{8}-\sqrt{7})}\\\\
=\frac{\sqrt{16}-\sqrt{14}+\sqrt{56}-7}{(8-7)}\\\\
=\frac{4-\sqrt{14}+\sqrt{4*14}-7}{(1)}\\\\
=4-\sqrt{14}+2\sqrt{14}-7\\\\
=-3+\sqrt{14}\\\\
=\sqrt{14}-3\\\\$$
$$\frac{\sqrt{2}+\sqrt{7}}{\sqrt{8}+\sqrt{7}}\\\\
=\frac{(\sqrt{2}+\sqrt{7})(\sqrt{8}-\sqrt{7})}{(\sqrt{8}+\sqrt{7})(\sqrt{8}-\sqrt{7})}\\\\
=\frac{\sqrt{16}-\sqrt{14}+\sqrt{56}-7}{(8-7)}\\\\
=\frac{4-\sqrt{14}+\sqrt{4*14}-7}{(1)}\\\\
=4-\sqrt{14}+2\sqrt{14}-7\\\\
=-3+\sqrt{14}\\\\
=\sqrt{14}-3\\\\$$