`\sqrt{3-2\sqrt{2}}/\sqrt{17-12\sqrt{2}}-\sqrt{3+2\sqrt{2}}/\sqrt{17+12\sqrt{2}}`
`=\sqrt{1-2\sqrt{2}+2}/\sqrt{3-12\sqrt{2}+8}-\sqrt{1+2\sqrt{2}+2}/\sqrt{3+12\sqrt{2}+8}`
`=\sqrt{(1-\sqrt{2})^{2}}/\sqrt{(3-2\sqrt{2})^{2}}-\sqrt{(1+\sqrt{2})^{2}}/\sqrt{(3+2\sqrt{2})^{2}}`
`=|1-\sqrt{2}|/|3-2\sqrt{2}|-|1+\sqrt{2}|/|3+2\sqrt{2}|`
`=(\sqrt{2}-1)/(3-2\sqrt{2})-(1+\sqrt{2})/(3+2\sqrt{2})`
`=((\sqrt{2}-1)(3+2\sqrt{2})-(1+\sqrt{2})(3-2\sqrt{2}))/((3-2\sqrt{2})(3+2\sqrt{2}))`
`=(\sqrt{2}+1-\sqrt{2}+1)/((3-2\sqrt{2})(3+2\sqrt{2}))`
`=2/((3-2\sqrt{2})(3+2\sqrt{2}))`
`=2/1`
`=2`
