`B = 15/(sqrt6 - 1) + 4/(sqrt6 - 2) - 12sqrt{2/3}`
`= (15(sqrt6 + 1))/((sqrt6 - 1)(sqrt6 + 1)) + (4(sqrt6 + 2))/((sqrt6 - 2)(sqrt6 + 2)) - 12sqrt{1/9}sqrt6`
`= (15(sqrt6 + 1))/5 + (4(sqrt6 + 2))/2 - 4sqrt6`
`= 3(sqrt6 + 1) + 2(sqrt6 + 2) - 4sqrt6`
`= 3sqrt6 + 3 + 2sqrt6 + 4 - 4sqrt6`
`= sqrt6 + 7`
Vậy `B = sqrt6 + 7`
`C = 2/(sqrt10 + 5) + 5/(sqrt10 - 2) - 7/(sqrt10)`
`= 2/(sqrt5(sqrt2 + sqrt5)) + 5/(sqrt2(sqrt5 - sqrt2)) - 7/(sqrt10)`
`= (2. sqrt2(sqrt5 - sqrt2))/(sqrt5(sqrt2 + sqrt5). sqrt2(sqrt5 - sqrt2)) + (5. sqrt5(sqrt5 + sqrt2))/(sqrt2(sqrt5 - sqrt2). sqrt5(sqrt5 + sqrt2)) + (7(sqrt5 + sqrt2)(sqrt5 - sqrt2))/(sqrt10. (sqrt5 + sqrt2)(sqrt5 - sqrt2))`
`= (2sqrt10 - 4)/(3sqrt10) + (5sqrt10 + 25)/(3sqrt10) - 21/(3sqrt10)`
`= (2sqrt10 - 4 + 5sqrt10 + 25 - 21)/(3sqrt10)`
`= (7sqrt10)/(3sqrt10)`
`= 7/3`
Vậy `C = 7/3`
`D = sqrt{2a}.sqrt{10a} - sqrt{45a^2} + a/(sqrt5 - 2)(a > 0)`
`= sqrt{20a^2} - sqrt{9a^2}sqrt5 + (a(sqrt5 + 2))/((sqrt5 - 2)(sqrt5 + 2))`
`= sqrt{4a^2}sqrt5 - 3asqrt5 + (asqrt5 + 2a)/1`
`= 2asqrt5 - 3asqrt5 + asqrt5 + 2a`
`= 2a`
Vậy `D = 2a`
