`a)`
`2/(1-sqrt2) + (6+2sqrt2)/(3+sqrt2)`
`= (2(1+sqrt2))/((1-sqrt2)(1+sqrt2)) + ((6+2sqrt2)(3-sqrt2))/((3+sqrt2)(3-sqrt2))`
`= (2(1+sqrt2))/(1^2 - (sqrt2)^2) + ((6+2sqrt2)(3-sqrt2))/(3^2 - (sqrt2)^2)`
`= -2(1+sqrt2) + (18-6sqrt2+6sqrt2-4)/7`
`= -2 - 2sqrt2 + 14/7`
`= -2 - 2sqrt2 + 2`
`= -2sqrt2`
`b)`
`1/(1-sqrt2+sqrt3) - 1/(1-sqrt2-sqrt3)`
`= (1(1-sqrt2-sqrt3))/((1-sqrt2+sqrt3)(1-sqrt2-sqrt3)) - (1(1-sqrt2+sqrt3))/((1-sqrt2-sqrt3)(1-sqrt2+sqrt3))`
`= (1-sqrt2-sqrt3)/((1-sqrt2)^2-sqrt3^2) - (1-sqrt2+sqrt3)/((1-sqrt2)^2-sqrt3^2)`
`= (1-sqrt2-sqrt3)/(-2sqrt2) - (1-sqrt2+sqrt3)/(-2sqrt2)`
`= -((1-sqrt2-sqrt3)sqrt2)/4 + ((1-sqrt2+sqrt3)sqrt2)/4`
`= -(sqrt2-2-sqrt6)/4 + (sqrt2-2+sqrt6)/4`
`= (-(sqrt2-2sqrt6)+sqrt2-2+sqrt6)/4`
`= (-sqrt2+2+sqrt6+sqrt2-2+sqrt6)/4`
`= (2sqrt6)/4`
`= sqrt6/2`