\frac{\sqrt{32}+\sqrt{2}}{\sqrt{2}}=\frac{\sqrt{2}(\sqrt{16}+1}{\sqrt{2}}=\sqrt{16}+1=4+1=5
\frac{\sqrt{27}-\sqrt{12}}{\sqrt{3}}=\frac{\sqrt{3}(\sqrt{9}-\sqrt{4}}{\sqrt{3}}=\sqrt{9}-\sqrt{4}=3-2=1
\frac{2\sqrt{50}-\sqrt{75}}{2\sqrt{2}}=\frac{2\sqrt{2*25}-\sqrt{3*25}}{2\sqrt{2}}=\frac{2*5\sqrt{2}-5\sqrt{3}}{2\sqrt{2}}=\frac{10\sqrt{2}-5\sqrt{3}}{2\sqrt{2}}=\frac{(10\sqrt{2}-5\sqrt{3})*\sqrt{2}}{2\sqrt{2}*\sqrt{2}}=\frac{20-5\sqrt{6}}{4}