Đáp án + Giải thích các bước giải:
`4/(sqrt5-sqrt2)+3/(sqrt5-2)-2/(sqrt3-2)+(sqrt3-1)/6`
`=[4(sqrt5+sqrt2)]/[(sqrt5-sqrt2)(sqrt5+sqrt2)]+[3(sqrt5+2)]/[(sqrt5-2)(sqrt5+2)]-[2(sqrt3+2)]/[(sqrt3-2)(sqrt3+2)]+(sqrt3-1)/6`
`=[4(sqrt5+sqrt2)]/(5-2)+[3(sqrt5+2)]/(5-4)-[2(sqrt3+2)]/(3-4)+(sqrt3-1)/6`
`=[4(sqrt5+sqrt2)]/3+[3(sqrt5+2)]/1-[-2(sqrt3+2)]/1+(sqrt3-1)/6`
`=[4*2(sqrt5+sqrt2)]/6+[3*6(sqrt5+2)]/6-[-2*6(sqrt3+2)]/6+(sqrt3-1)/6`
`=[8(sqrt5+sqrt2)]/6+[18(sqrt5+2)]/6-[-12(sqrt3+2)]/6+(sqrt3-1)/6`
`=(8sqrt5+8sqrt2+18sqrt5+36-(-12sqrt3-24)+sqrt3-1)/6`
`=(8sqrt5+8sqrt2+18sqrt5+36+12sqrt3+24+sqrt3-1)/6`
`=(26sqrt5+8sqrt2+13sqrt3+59)/6`.
