`1)P=(\frac{\sqrt{x}}{\sqrt{x}+4}+\frac{4}{\sqrt{x}-4}):\frac{x+16}{\sqrt{x}+2}`
`{(\sqrt{x}+4\ne0),(\sqrt{x}-4\ne0),(\sqrt{x}+2\ne0),(x>=0):}`
`<=>{(x\ne16),(x>=0):}`
`P=(\frac{\sqrt{x}}{\sqrt{x}+4}+\frac{4}{\sqrt{x}-4}):\frac{x+16}{\sqrt{x}+2}`
`=(\frac{\sqrt{x}(\sqrt{x}-4)+4(\sqrt{x}+4)}{x-16}.\frac{\sqrt{x}+2}{x+16}`
`=\frac{x-4\sqrt{x}+4\sqrt{x}+16}{x-16}.\frac{\sqrt{x}+2}{x+16}`
`=\frac{(x+16)(\sqrt{x}+2)}{(x-16)(x+16)}`
`=\frac{\sqrt{x}+2}{x-16}`
`2)Q=P.(\frac{\sqrt{x}+4}{\sqrt{x}+2}-1)`
`=\frac{\sqrt{x}+2}{x-16}.(\frac{\sqrt{x}+4-\sqrt{x}-2}{\sqrt{x}+2})`
`=\frac{\sqrt{x}+2}{x-16}.\frac{2}{\sqrt{x}+2}`
`=\frac{2}{x-16}`
Để `Q∈Z` thì `2\vdots x-16`
`<=>x-16∈Ư(2)`
`=>x-16∈{±1;±2}`
`<=>x∈{-1+16;1+16;-2+16;2+16}`
`->x∈{15;17;14;18}`
Vậy `x∈{15;17;14;18}` thì `Q∈Z`
