Đáp án+Giải thích các bước giải:
`a)x=9`
`=>sqrtx=3`
`=>A=(3+2)/(3+1)=5/4`
Vậy `x=9` thì `A=5/4.`
`b)B=2/(sqrtx+1)+(x+3)/(x-1)`
`=(2(sqrtx-1))/((sqrtx-1)(sqrtx+1))+(x+3)/((sqrtx-1)(sqrtx+1))`
`=(2sqrtx-2+x+3)/((sqrtx-1)(sqrtx+1))`
`=(x+2sqrtx+1)/((sqrtx-1)(sqrtx+1))`
`=(sqrtx+1)^2/((sqrtx-1)(sqrtx+1))`
=(sqrtx+1)/(sqrtx-1)`
`c)C=A.B=(sqrtx+2)/(sqrtx+1)*(sqrtx+1)/(sqrtx-1)`
`C=(sqrtx+2)/(sqrtx-1) in ZZ`
`=>sqrtx+2 vdots sqrtx-1`
`=>sqrtx-1+3 vdots sqrtx-1`
`=>3 vdots sqrtx-1`
`=>sqrtx-1 in Ư(3)={+-1,+-3}`
Mà `x max=>sqrtx max`
`=>sqrtx-1=3`
`=>sqrtx=4`
`=>x=16`
Vậy `x=16` là số lớn nhất để C=A.B có giá trị nguyên.