$\frac{\sqrt{8}+\sqrt{6}}{\sqrt{2}}=\frac{\left(\sqrt{8}+\sqrt{6}\right)\cdot \sqrt{2}}{{\sqrt{2}}^2}=\frac{\sqrt{8}\cdot \sqrt{2}+\sqrt{6}\cdot \sqrt{2}}{2}=\frac{\sqrt{8\cdot 2}+\sqrt{6\cdot 2}}{2}=\frac{\sqrt{16}+\sqrt{12}}{2}=\frac{4+\sqrt{4\cdot 3}}{2}=\frac{4+\sqrt{4}\cdot \sqrt{3}}{2}=\frac{4+2\sqrt{3}}{2}=2+\sqrt{3}$