`a) 2/(\sqrt{11}-\sqrt{17})`

`= (2(\sqrt{11}+\sqrt{17}))/(11-17)`

`= (2(\sqrt{11}+\sqrt{17}))/(-6)`

`= -(\sqrt{11}+\sqrt{17})/3`

`b) (\sqrt{7})/(3+\sqrt{7})`

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

`= (3\sqrt{7}-7)/(9 - 7)`

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

`c) (\sqrt{7}+1)/(\sqrt{7}-1)`

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

`= ( 8 + 2\sqrt{7})/( 7 - 1 )`

`= ( 2( 4 + \sqrt{7}))/6`

`= ( 4 + \sqrt{7})/3`

`d) ( \sqrt{11}-1)/(\sqrt{11}+1)`

`=((\sqrt{11}-1)^2)/((\sqrt{11}+1)(\sqrt{11}-1))`

`= ( 12 - 2\sqrt{11})/( 11 - 1 )`

`= ( 2( 6 - \sqrt{11}))/10`

`= ( 6 - \sqrt{11})/5`

`e) ( \sqrt{11}-\sqrt{13})/(\sqrt{11}+\sqrt{13})`

`= ((\sqrt{11}-\sqrt{13})^2)/((\sqrt{11}+\sqrt{13})(\sqrt{11}-\sqrt{13}))`

`= ( 24 - 2\sqrt{143})/( 11 - 13 )`

`= ( 2( 12 - \sqrt{143}))/(-2)`

`= \sqrt{143} - 12`

`f) ( \sqrt{15}+\sqrt{17})/(\sqrt{15}-\sqrt{17})`

`= ((\sqrt{15}+\sqrt{17})^2)/(( \sqrt{15} - \sqrt{17})( \sqrt{15} + \sqrt{17}))`

`=( 32 + 2\sqrt{255})/( 15 - 17 )`

`= ( 2( 16 + \sqrt{255}))/(-2)`

`= -16 - \sqrt{255}`

`g) ( \sqrt{5} + 1 )/( 4 - \sqrt{5})`

`= (( \sqrt{5} + 1 )( 4 + \sqrt{5}))/(( 4 - \sqrt{5})( 4 + \sqrt{5}))`

`= ( 4\sqrt{5} + 4 + 5 + \sqrt{5})/( 16 - 5 )`

`= ( 9 + 5\sqrt{5})/11`

`h) ( \sqrt{7}+1)/(6-\sqrt{7})`

`= ((\sqrt{7}+1)(6+\sqrt{7}))/((6-\sqrt{7})(6+\sqrt{7}))`

`= ( 6\sqrt{7}+6 + 7 + \sqrt{7})/( 36 - 7 )`

`= ( 13 + 7\sqrt{7})/29`