`\frac{6+4\sqrt{2}}{\sqrt{2}+\sqrt{6+4\sqrt{2}}}+\frac{6-4\sqrt{2}}{\sqrt{2}-\sqrt{6-4\sqrt{2}}}`
`=\frac{6+4\sqrt{2}}{\sqrt{2}+\sqrt{(2+\sqrt{2})^2}}+\frac{6-4\sqrt{2}}{\sqrt{2}-\sqrt{(2-\sqrt{2})^2}}`
`=\frac{6+4\sqrt{2}}{\sqrt{2}+|2+\sqrt{2}|}+\frac{6-4\sqrt{2}}{\sqrt{2}-|2-\sqrt{2}|}`
`=\frac{6+4\sqrt{2}}{\sqrt{2}+2+\sqrt{2}}+\frac{6-4\sqrt{2}}{\sqrt{2}-2+\sqrt{2}}`
`=\frac{(6+4\sqrt{2})(2\sqrt{2}-2)+(6-4\sqrt{2})(2\sqrt{2}+2)}{8-4}`
`=\frac{12\sqrt{2}-12+16-8\sqrt{2}+12\sqrt{2}+12-16-8\sqrt{2}}{4}`
`=\frac{8\sqrt{2}}{4}`
`=2\sqrt{2}`
