`a)`

`a/[3-2sqrt2]`

`= [a(3+2sqrt2)]/[9-8]`

`= 3a+2asqrt2`

`b)`

`[5sqrt3-3sqrt5]/[5sqrt3+3sqrt5]`

`= [sqrt15(sqrt5-sqrt3)]/[sqrt15(sqrt5+sqrt3)]`

`= [sqrt5-sqrt3]/[sqrt5+sqrt3]`

`= [(sqrt5-sqrt3)^2]/[5-3]`

`= [5-2sqrt15+3]/2`

`= [8-2sqrt15]/2`

`= 4-sqrt15`

`c)`

`[sqrt2]/[1-sqrt2+sqrt3]`

`= [sqrt2(1-sqrt2-sqrt3)]/[(1-sqrt2)^2-3]`

`= [sqrt2-2-sqrt6]/[-2sqrt2]`

`= [sqrt2(sqrt2-2-sqrt6)]/[-4]`

`= [2-2sqrt2-2sqrt3]/[-4]`

`= [1-sqrt2-sqrt3]/[-2]`

`= [sqrt3+sqrt2-1]/2`