$\displaystyle \begin{array}{{>{\displaystyle}l}} M=\left(\frac{\sqrt{a} +2}{a+2\sqrt{a} +1} -\frac{\sqrt{a} -2}{a-1}\right) .\frac{\sqrt{a} +1}{\sqrt{a}} \ \\ DK\ :x >0;\ a\#1\\ M=\left(\frac{\sqrt{a} +2}{\left(\sqrt{a} +1\right)^{2}} -\frac{\sqrt{a} -2}{\left(\sqrt{a} -1\right)\left(\sqrt{a} +1\right)}\right) .\frac{\sqrt{a} +1}{\sqrt{a}} \ \\ M=\frac{\left(\sqrt{a} +2\right)\left(\sqrt{a} -1\right) -\left(\sqrt{a} -2\right)\left(\sqrt{a} +1\right)}{( a-1)\left(\sqrt{a} +1\right)} .\frac{\sqrt{a} +1}{\sqrt{a}} \ \\ M=\frac{a+\sqrt{a} -2-a+\sqrt{a} +2}{( a-1)\sqrt{a}}\\ M=\frac{2\sqrt{a}}{( a-1)\sqrt{a}} =\frac{2}{a-1} \ \\ c) \ A\ thuộc\ Z\ và\ M\ nguyên\ nên\ a-1\ là\ ước\ của\ 2\ \\ Do\ đó\ :\ \\ a-1=1\ \rightarrow a=2\ \\ a-1=-1\ \rightarrow x=0\\ a-1=2\rightarrow a=3\\ a-1=-2\ \rightarrow a=-1\ \end{array}$
