`a)`

`(sqrt5-sqrt3)/(sqrt5+sqrt3)+(sqrt5+sqrt3)/(sqrt5-sqrt3)-(sqrt5+1)/(sqrt5-1)`

`=((sqrt5-sqrt3)(sqrt5-sqrt3))/((sqrt5+sqrt3)(sqrt5-sqrt3))+((sqrt5+sqrt3)(sqrt5+sqrt3))/((sqrt5+sqrt3)(sqrt5-sqrt3))+((sqrt5+1)(sqrt5+1))/((sqrt5-1)(sqrt5+1))`

`=((sqrt5-sqrt3)^2+(sqrt5+sqrt3)^2)/2-((sqrt5+1)^2)/4`

`=(5-2sqrt15+3+5+2sqrt15+3)/2-(5+2sqrt5+1)/4`

`=16/2-(6+2sqrt5)/4=(32-6-2sqrt5)/4`

`=(26-2sqrt5)/4=(13-sqrt5)/2`

`b)`

`((9-2sqrt14)/(sqrt7-sqrt2))^2+((9+2sqrt14)/(sqrt7+sqrt2))^2`

`=((7-2sqrt(7.2)+2)/(sqrt7-sqrt2))^2+((7+2sqrt(7.2)+2)/(sqrt7+sqrt2))^2`

`=(((sqrt7-sqrt2)^2)/(sqrt7-sqrt2))^2+(((sqrt7+sqrt2)^2)/(sqrt7+sqrt2))^2`

`=(sqrt7-sqrt2)^2+(sqrt7+sqrt2)^2`

`=7-2sqrt14+2+7+2sqrt14+2`

`=18`

`a) (\sqrt{5}-\sqrt{3})/(\sqrt{5}+\sqrt{3})+(\sqrt{5}+\sqrt{3})/(\sqrt{5}-\sqrt{3})-(\sqrt{5}+1)/(\sqrt{5}-1)`

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

`=(5+3-2\sqrt{15})/2+(5+3+2\sqrt{15})/2-(5+1+2\sqrt{5})/4`

`=(8-2\sqrt{15})/2+(8+2\sqrt{15})/2-(6+2\sqrt{5})/4`

`=4-\sqrt{15}+4+\sqrt{15}-3/2-\sqrt{5}/2`

`=(13-\sqrt{5})/2`

`b) ((9-2sqrt{14})/(\sqrt{7}-\sqrt{2}))^2+((9+2sqrt{14})/(\sqrt{7}+\sqrt{2}))^2`

`=((9-2sqrt{14})/(\sqrt{7}-\sqrt{2}))^2+(2(9-2\sqrt{14})(9+2\sqrt{14}))/((\sqrt{7}-\sqrt{2})(\sqrt{7}+\sqrt{2}))+((9+2sqrt{14})/(\sqrt{7}+\sqrt{2}))^2-10`

`=((9-2sqrt{14})/(\sqrt{7}-\sqrt{2})+(9+2sqrt{14})/(\sqrt{7}+\sqrt{2}))^2-10`

`=(((9-2\sqrt{14})(\sqrt{7}+\sqrt{2})+(9+2sqrt{14})(\sqrt{7}-\sqrt{2}))/(7-2))^2-10`

`=((9sqrt{7}+9sqrt{2}-14sqrt{2}-4sqrt{7}+9sqrt{7}-9sqrt{2}+14sqrt{2}-4sqrt{7})/5)^2-10`

`=((18sqrt{7}-8sqrt{7})/5)^2-10`

`=((10sqrt{7})/5)^2-10`

`=(2sqrt{7})^2-10`

`=28-10`

`=18`