`1. 3/(\sqrt{5} = (3\sqrt{5})/5`

`2. 5/(sqrt{10}) = (5\sqrt{10})/10 = (\sqrt{10})/2`

`3. 3/(2\sqrt{5}) = (3\sqrt{5})/10`

`4. 5/(2\sqrt{3}) = (5\sqrt{3})/6`

`5. 2/(\sqrt{3} - 1) = (2(\sqrt{3} + 1))/((\sqrt{3} - 1 ) (\sqrt{3} + 1)) = \sqrt{3} + 1`

`6. 3(\sqrt{3} + 2) = (3(\sqrt{3} - 2))/((\sqrt{2} + 2)(\sqrt{3} - 2)) = -3\sqrt{3} + 6`

`7. (3\sqrt{2} )/(\sqrt{3} + 1) = (3\sqrt{2}(\sqrt{3} -1))/((\sqrt{3} + 1)(sqrt{3} - 1)) = (3\sqrt{2} (\sqrt{3} - 1))/2`

`8. (3\sqrt{2})/(\sqrt{5} + 3) = (3sqrt{2} (\sqrt{5} - 3))/(-4) =  (-3\sqrt{2} (\sqrt{5} - 3))/4`

`9. 2/(\sqrt{6}  - \sqrt{5} ) = (2\sqrt{6} + \sqrt{5}) = 2\sqrt{5} + 2\sqrt{5}`

`10. 1/(sqrt{3} + \sqrt{2} = (\sqrt{3} - \sqrt{2})/1 = \sqrt{3} - \sqrt{2}`

`11. 3/(\sqrt{10} + \sqrt{7}) = (3(\sqrt{10} - \sqrt{7}) )/3 = \sqrt{10} - \sqrt{7}`

`12. (-\sqrt{4})/(\sqrt{7} - \sqrt{2}) = (-2(\sqrt{7} + \sqrt{2}))/5`

`@Dark`