`a)`
`(3+sqrt3)/(1+sqrt3)=(sqrt3(sqrt3+1))/(sqrt3+1)=sqrt3`
`b)`
`(sqrt15-sqrt3)/(1-sqrt5)=(sqrt3(sqrt5-1))/(-(sqrt5-1))`
`=(sqrt3)/(-1)=-sqrt3`
`c)`
`(2sqrt3-sqrt6)/(sqrt3-2)`
`=((2sqrt3-sqrt6)(sqrt3+2))/((sqrt3-2)(sqrt3+2))`
`=(6-sqrt18+4sqrt3-2sqrt6)/(-1)`
`=-(6-3sqrt2+4sqrt3-2sqrt6)`
`=-6+3sqrt2-4sqrt3+2sqrt6`
`d)`
`(sqrt14-sqrt7)/(1-sqrt2)`
`=(sqrt7(sqrt2-1))/(-(sqrt2-1))`
`=(sqrt7)/(-1)=-sqrt7`