1) `(5\sqrt2-2\sqrt5)/(\sqrt5-\sqrt2)+6/(2-\sqrt10)`
`=(\sqrt5.\sqrt5. \sqrt2-\sqrt2 . \sqrt2. \sqrt5)/(\sqrt5-\sqrt2)+(6(2+\sqrt10))/((2-\sqrt10)(2+\sqrt10))`
`=(\sqrt5.\sqrt10-\sqrt2.\sqrt10)/(\sqrt5-\sqrt2)+(6(2+\sqrt10))/(-6)`
`=(\sqrt10(\sqrt5-\sqrt2))/(\sqrt5-\sqrt2)-(2+\sqrt10)`
`=\sqrt10-2-\sqrt10=-2`
2) `((\sqrt14-\sqrt7)/(1-\sqrt2)+(\sqrt15-\sqrt5)/(1-\sqrt3)):1/(\sqrt7-\sqrt5)`
`=((-\sqrt7(1-\sqrt2))/(1-\sqrt2)+(-\sqrt5(1-\sqrt3))/(1-\sqrt3)).(\sqrt7-\sqrt5)`
`=(-\sqrt7-\sqrt5)(\sqrt7-\sqrt5)`
`=-(\sqrt7+\sqrt5)(\sqrt7-\sqrt5)`
`=-2`
3) `(\sqrt5+2).((\sqrt5+2)^2-8\sqrt5)/(\sqrt5-2)`
`=(\sqrt5+2).(5+4\sqrt5+4-8\sqrt5)/(\sqrt5-2)`
`=(\sqrt5+2). (9-4\sqrt5)/(\sqrt5-2)`
`=(\sqrt5+2). (5-2.2.\sqrt5+4)/(\sqrt5-2)`
`=(\sqrt5+2) . (\sqrt5-2)^2/(\sqrt5-2)`
`=(\sqrt5+2)(\sqrt5-2)=1`
4) `((\sqrt3-\sqrt2)^2+4\sqrt6)/(\sqrt3+\sqrt2)^2.(\sqrt3-\sqrt2)`
`=(3-2\sqrt6+2+4\sqrt6)/(\sqrt3+\sqrt2)^2.(\sqrt3-\sqrt2)`
`=(5+2\sqrt6)/(\sqrt3+\sqrt2)^2.(\sqrt3-\sqrt2)`
`=(3+2.\sqrt3 . \sqrt2 + 2)/(\sqrt3+\sqrt2).(\sqrt3-\sqrt2)`
`=(\sqrt3+\sqrt2)^2/(\sqrt3+\sqrt2)^2 . (\sqrt3-\sqrt2)`
`=1.(\sqrt3-\sqrt2)=\sqrt3-\sqrt2 `