Đáp án+Giải thích các bước giải:
`Q=((sqrtx+2)/(x+2sqrtx+1)-(sqrtx-2)/(x-1))(x+sqrtx)(x>0,x ne 1)`
`a)Q=((sqrtx+2)/(sqrtx+1)^2-(sqrtx-2)/((sqrtx-1)(sqrtx+1))*(sqrtx(sqrtx+1))`
`Q=(((sqrtx+2)(sqrtx-1))/((sqrtx+1)^2(sqrtx-1))-((sqrtx-2)(sqrtx+2))/((sqrtx+1)^2(sqrtx-1)))*sqrtx*(sqrtx+1)`
`Q=((sqrtx+2)(sqrtx-1)-(sqrtx-2)(sqrtx+1))/((sqrtx+1)^2(sqrtx-1))*sqrtx*(sqrtx+1)`
`Q=(x+sqrtx-2-(x-sqrtx-2))/((sqrtx-1)(sqrtx+1))*sqrtx`
`Q=(2sqrtx)/((sqrtx-1)(sqrtx+1))*sqrtx`
`Q=(2x)/(x-1)`
`b)` ĐK:`x>0,x\ne1,x\inZZ`
`=>x>=2,x in ZZ`
`Q\inZZ`
`=>2xvdots x-1`
`=>2x-2+2\vdots x-1`
`=>2\vdots x-1`
`=>x-1\in Ư(2)={+-1,+-2}`
`*x-1=1=>x=2(tm)`
`*x-1=-1=>x=0(ktm)`
`*x-1=2=>x=3(tm)`
`*x-1=-2=>x=-1(ktm)`
Vậy với `x in {2;3}` thì `Q ` nguyên.
