`2/(3\sqrt2-4)-2/(3\sqrt2+4)`
`=(2(3\sqrt2+4))/((3\sqrt2-4)(3\sqrt2+4))-(2(3\sqrt2-4))/((3\sqrt2-4)(3\sqrt2+4))`
`=(6\sqrt2+8)/(18-16)-(6\sqrt2-8)/(18-16)`
`=(6\sqrt2+8-6\sqrt2+8)/2`
`=16/2`
`=8`
`1/(\sqrt5+\sqrt7)+2/(1-\sqrt7)`
`=(1(\sqrt5-\sqrt7))/((\sqrt5+\sqrt7)(\sqrt5-\sqrt7))+(2(1+\sqrt7))/((1-\sqrt7)(1+\sqrt7))`
`=-(\sqrt5-\sqrt7)/2-(2+2\sqrt7)/6`
`=(-3(\sqrt5-\sqrt7))/6-(2+2\sqrt7)/6`
`=(-3\sqrt5+3\sqrt7-2-2\sqrt7)/6`
`=(-3\sqrt5+\sqrt7-2)/6`