a) Với \(a>0;a\neq1\), ta có:
\(M=\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{2\sqrt{a}-1}{a-\sqrt{a}}\)
\(\Leftrightarrow\) \(M=\dfrac{\sqrt{a}}{\sqrt{a}-1}-\dfrac{2\sqrt{a}-1}{\sqrt{a}(\sqrt{a}-1)}\)
\(\Leftrightarrow\) \(M=\dfrac{a-2\sqrt{a}+1}{\sqrt{a}(\sqrt{a}-1)}\)
\(\Leftrightarrow\) \(M=\dfrac{(\sqrt{a}-1)^2}{\sqrt{a}(\sqrt{a}-1)}\)
\(\Leftrightarrow\) \(M=\dfrac{\sqrt{a}-1}{\sqrt{a}}\)
b) Ta có: \(M=-3\)
\(\Leftrightarrow\) \(\dfrac{\sqrt{a}-1}{\sqrt{a}}=-3\)
\(\Leftrightarrow\) \(\sqrt{a}-1=-3\sqrt{a}\)
\(\Leftrightarrow\) \(4\sqrt{a}=1\)
\(\Leftrightarrow\) \(\sqrt{a}=\dfrac{1}{4}\)
\(\Leftrightarrow\) \(a=\dfrac{1}{16}\)
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