Đáp án + Giải thích các bước giải:
`a)` `(sqrta+sqrtb)/(2sqrta-2sqrtb)-(sqrta-sqrtb)/(2sqrta+2sqrtb)-(2b)/(b-a)(a,b>0,aneb)`
`=(sqrta+sqrtb)/[2(sqrta-sqrtb)]-(sqrta-sqrtb)/[2(sqrta+sqrtb)]+(2b)/(a-b)`
`=[(sqrta+sqrtb)(sqrta+sqrtb)]/[2(sqrta-sqrtb)(sqrta+sqrtb)]-[(sqrta-sqrtb)(sqrta-sqrtb)]/[2(sqrta-sqrtb)(sqrta+sqrtb)]+(2b*2)/[2(sqrta-sqrtb)(sqrta+sqrtb)]`
`=[a+2sqrt(ab)+b-(a-2sqrt(ab)+b)+4b]/[2(sqrta-sqrtb)(sqrta+sqrtb)]`
`=(a+2sqrt(ab)+b-a+2sqrt(ab)-b+4b)/[2(sqrta-sqrtb)(sqrta+sqrtb)]`
`=(4sqrt(ab)+4b)/[2(sqrta-sqrtb)(sqrta+sqrtb)]`
`=[4sqrtb(sqrta+sqrtb)]/[2(sqrta-sqrtb)(sqrta+sqrtb)]`
`=(4sqrtb)/[2(sqrta-sqrtb)]=(2sqrtb)/(sqrta-sqrtb)`(đpcm)
`b)` `((asqrta+bsqrtb)/(sqrta+sqrtb)-sqrt(ab))((sqrta+sqrtb)/(a-b))^2(a,b>0,aneb)`
`=((asqrta+bsqrtb)/(sqrta+sqrtb)-[sqrt(ab)(sqrta+sqrtb)]/[(sqrta+sqrtb)])((sqrta+sqrtb)/[(sqrta+sqrtb)(sqrta-sqrtb)))^2`
`=(asqrta+bsqrtb-(asqrtb+bsqrta))/(sqrta+sqrtb)*(1/(sqrta-sqrtb))^2`
`=(asqrta+bsqrtb-asqrtb-bsqrta)/(sqrta+sqrtb)*1/(sqrta-sqrtb)^2`
`=[a(sqrta-sqrtb)+b(sqrtb-sqrta)]/(sqrta+sqrtb)*1/[(sqrta-sqrtb)^2]`
`=[a(sqrta-sqrtb)-b(sqrta-sqrtb)]/[(sqrta+sqrtb)]*1/[(sqrta-sqrtb)^2]`
`=[(sqrta-sqrtb)(a-b)]/[(sqrta+sqrtb)]*1/[(sqrta-sqrtb)^2]`
`=[(sqrta-sqrtb)(sqrta+sqrtb)(sqrta-sqrtb)]/(sqrta+sqrtb)*1/[(sqrta-sqrtb)^2]`
`=(sqrta-sqrtb)^2*1/[(sqrta-sqrtb)^2]=1` (đpcm).
