`a) 3/(2sqrt5) = (3.sqrt5)/(2sqrt5.sqrt5) = (3.sqrt5)/(2sqrt5^2) = (3.sqrt5)/(2.5) = (3.sqrt5)/(10)`
`b)(2sqrt3)/(sqrt2)=(2sqrt3.sqrt2)/(sqrt2.sqrt2)=(2sqrt3.2)/(sqrt2^2)=(2sqrt6)/(2)=sqrt6`
`c) (5)/(2-sqrt3)=(5(2+sqrt3))/((2-sqrt3)(2+sqrt3))=(10+5sqrt3)/(4-sqrt3^2)=(10+5sqrt3)/(4-3)=10+5sqrt3`
`d)3/(sqrt2 - sqrt3)=(3(sqrt2 + sqrt3))/((sqrt2 +sqrt3)(sqrt2 - sqrt3))=(3sqrt2 + 3sqrt3)/(sqrt2^2-sqrt3^2)`
`=(3sqrt2 + 3sqrt3)/(2-3)=(3sqrt2 + 3sqrt3)/(-1)=-3sqrt2 - 3sqrt3`
`e) (3-sqrt3)/(2sqrt3)=((3-sqrt3).sqrt3)/(2sqrt3.sqrt3)=(3sqrt3-sqrt3^2)/(2sqrt3^2)=(3sqrt3-3)/(2.3)`
`=(3(sqrt3-1))/(3.2)=(sqrt3-1)/(2)`
`f) (5-sqrt5)/(1-sqrt5)=((5-sqrt5)(1+sqrt5))/((1-sqrt5)(1+sqrt5))=(sqrt5(sqrt5-1)(sqrt5+1))/(1^2-sqrt5^2)`
`=(sqrt5(sqrt5^2-1^2))/(1-5)=(sqrt5(5-1))/(-4)=(4sqrt5)/(-4)=-sqrt5`
`g) (2)/(2-3sqrt5)=(2.(2+3sqrt5))/((2-3sqrt5)(2+3sqrt5))=(4+6sqrt5)/(2^2-(3sqrt5)^2)`
`=(4+6sqrt5)/(4-45)=(4+6sqrt5)/(-41)=(-4-6sqrt5)/(41)`
