Đáp án+Giải thích các bước giải:
`d)(3/(sqrt5-sqrt2)+4/(sqrt6+sqrt2))(sqrt3-1)^2`
`=((3(sqrt5+sqrt2))/(5-2)+(4(sqrt6-sqrt2))/(6-2))(sqrt3-1)^2`
`=((3(sqrt5+sqrt2))/3+(4(sqrt6-sqrt2))/4)(sqrt3-1)^2`
`=(sqrt5+sqrt2+sqrt6-sqrt2)(4-2sqrt3)`
`=(sqrt6+sqrt5)(4-2sqrt3)`
`=4sqrt6-6sqrt2+4sqrt5-2sqrt15`
`e)1/(1+sqrt2)+1/(sqrt2+sqrt3)+.......+1/(sqrt99+sqrt100)`
`=(sqrt2-1)/(2-1)+(sqrt3-sqrt2)/(3-2)+....+(sqrt100-sqrt99)/(100-99)`
`=sqrt2-1+sqrt3-sqrt2+.....+sqrt100-sqrt99`
`=10-1=9`
