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`i)(sqrt15-sqrt5)/(sqrt3-1)+(5-2sqrt5)/(2sqrt5-4)`

`=(sqrt5(sqrt3-1))/(sqrt3-1)+(5-2sqrt5)/(2sqrt5-4)`

`=sqrt5+(5-2sqrt5)/(2sqrt5-4)`

`=(2*sqrt{5^2}-4sqrt5)/(2sqrt5-4)+(5-2sqrt5)/(2sqrt5-4)`

`=(2*5-4sqrt5+5-2sqrt5)/(2sqrt5-4)`

`=(15-6sqrt5)/(2sqrt5-4)`

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

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

`=(sqrt5-sqrt3-sqrt5-sqrt3)/(5-3)`

`=(-2sqrt3)/2`

`=-sqrt3`

`l)1/(2+sqrt3)-1/(2-sqrt3)+5sqrt3`

`=(2-sqrt3)/((2-sqrt3)(2+sqrt3))-(2+sqrt3)/((2+sqrt3)(2-sqrt3))+5 sqrt3`

`=(2-sqrt3-2-sqrt3)/((2+sqrt3)(2-sqrt3))+5sqrt3`

`=(-2sqrt3)/(4-3)+5sqrt3`

`=-2sqrt3+5sqrt3`

`=3sqrt3`

`m)sqrt{9+4sqrt5}-sqrt5`

`=sqrt{5+2*2*sqrt5+2^2}-sqrt5`

`=sqrt{(sqrt5+2)^2}-sqrt5`

`=|sqrt5+2|-sqrt5`

`=sqrt5+2-sqrt5`

`=2`