`ĐKXĐ:a\ge0,a\ne1`
`a,A=({\sqrt{a}-2}/{a+2\sqrt{a}+1}-{\sqrt{a}+2}/{a-1}):{\sqrt{a}}/{a-1}`
`=[{\sqrt{a}-2}/{(\sqrt{a}+1)^2}-{\sqrt{a}+2}/{(\sqrt{a}+1)(\sqrt{a}-1)}]:{\sqrt{a}}/{(\sqrt{a}+1)(\sqrt{a}-1)}`
`=[{(\sqrt{a}-2)(\sqrt{a}-1)}/{(\sqrt{a}+1)^2(\sqrt{a}-1)}-{(\sqrt{a}+2)(\sqrt{a}+1)}/{(\sqrt{a}+1)^2(\sqrt{a}-1)}]:{\sqrt{a}}/{(\sqrt{a}+1)(\sqrt{a}-1)}`
`={(\sqrt{a}-2)(\sqrt{a}-1)-(\sqrt{a}+2)(\sqrt{a}+1)}/{(\sqrt{a}+1)^2(\sqrt{a}-1)}:{\sqrt{a}}/{(\sqrt{a}+1)(\sqrt{a}-1)}`
`={a-\sqrt{a}-2\sqrt{a}+2-(a+\sqrt{a}+2\sqrt{a}+2)}/{(\sqrt{a}+1)^2(\sqrt{a}-1)}:{\sqrt{a}}/{(\sqrt{a}+1)(\sqrt{a}-1)}`
`={a-\sqrt{a}-2\sqrt{a}+2-a-\sqrt{a}-2\sqrt{a}-2}/{(\sqrt{a}+1)^2(\sqrt{a}-1)}:{\sqrt{a}}/{(\sqrt{a}+1)(\sqrt{a}-1)}`
`={-6\sqrt{a}}/{(\sqrt{a}+1)^2(\sqrt{a}-1)}:{\sqrt{a}}/{(\sqrt{a}+1)(\sqrt{a}-1)}`
`={-6\sqrt{a}}/{(\sqrt{a}+1)^2(\sqrt{a}-1)}.{(\sqrt{a}+1)(\sqrt{a}-1)}/{\sqrt{a}}`
`={-6}/{\sqrt{a}+1}`
Vậy với `a\ge0,a\ne1` thì `A={-6}/{\sqrt{a}+1}`
`b,A\inZ⇔{-6}/{\sqrt{a}+1}\inZ`
`⇔\sqrt{a}+1\inƯ(-6)={-6;-3;-2;-1;1;2;3;6}`
`⇔\sqrt{a}\in{-7;-4;-3;-2;0;1;2;5}`
Mà `\sqrt{a}\ge0` với mọi `a\ge0`
`⇒\sqrt{a}\in{0;1;2;5}`
`⇒a\in{0;1;4;25}`
Mà `a\ge0,a\ne1,a\inZ`
`⇒a\in{0;4;25}(TM)`
Vậy với `a\in{0;4;25}` thì `A\inZ`
