Đáp án:
Giải thích các bước giải:
`M=(\frac{\sqrt{a}+2}{a+2\sqrt{a}+1}-\frac{\sqrt{a}-2}{a-1}).\frac{\sqrt{a}+1}{\sqrt{a}}`
a) ĐKXĐ:
\(\begin{cases} a+2\sqrt{a}+1 \ne 0\\a-1 \ne 0\\a>0\end{cases}\)
`⇔` \(\begin{cases} (\sqrt{a}+1)^2 \ne 0\\a \ne 1\\a>0\end{cases}\)
`⇒` \(\begin{cases} a \ne 1\\a>0\end{cases}\)
b) `M=[\frac{\sqrt{a}+2}{(\sqrt{a}+1)^2}-\frac{\sqrt{a}-2}{a-1}].\frac{\sqrt{a}+1}{\sqrt{a}}`
`M=[\frac{(\sqrt{a}+2)(\sqrt{a}-1)}{(\sqrt{a}+1)^2(\sqrt{a}-1)}-\frac{(\sqrt{a}+1)(\sqrt{a}-2)}{(\sqrt{a}+1)^2(\sqrt{a}-1)}].\frac{\sqrt{a}+1}{\sqrt{a}}`
`M=[\frac{a-\sqrt{a}+2\sqrt{a}-2}{(\sqrt{a}+1)^2(\sqrt{a}-1)}-\frac{a-2\sqrt{a}+\sqrt{a}-2}{(\sqrt{a}+1)^2(\sqrt{a}-1)}].\frac{\sqrt{a}+1}{\sqrt{a}}`
`M=[\frac{a+\sqrt{a}-2-a+\sqrt{a}+2}{(\sqrt{a}+1)^2(\sqrt{a}-1)}].\frac{\sqrt{a}+1}{\sqrt{a}}`
`M=\frac{2\sqrt{a}}{(\sqrt{a}+1)^2(\sqrt{a}-1)}.\frac{\sqrt{a}+1}{\sqrt{a}}`
`M=\frac{2}{a-1}`