\(a,A=\dfrac{x-1-4\sqrt{x}+\sqrt{x}+1}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}\cdot\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}\\ A=\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{\sqrt{x}\left(\sqrt{x}-2\right)}=\dfrac{\sqrt{x}-3}{\sqrt{x}-2}\\ b,x=9\Leftrightarrow\sqrt{x}=3\\ \Leftrightarrow A=\dfrac{3-3}{3-2}=0\\ c,A=\dfrac{5}{2}\Leftrightarrow2\left(\sqrt{x}-3\right)=5\left(\sqrt{x}-2\right)\\ \Leftrightarrow2\sqrt{x}-6=5\sqrt{x}-10\\ \Leftrightarrow3\sqrt{x}=4\Leftrightarrow x=\dfrac{16}{9}\left(tm\right)\)
a) \(A=\dfrac{x-1-4\sqrt{x}+\sqrt{x}+1}{x-1}.\dfrac{x-1}{x-2\sqrt{x}}\)
\(=\dfrac{x-3\sqrt{x}}{x-2\sqrt{x}}\)
b) \(A=\dfrac{x-3\sqrt{x}}{x-2\sqrt{x}}=\dfrac{9-3.3}{9-2.3}=\dfrac{0}{3}=0\)
c) \(A=\dfrac{x-3\sqrt{x}}{x-2\sqrt{x}}=\dfrac{5}{2}\)
\(\Leftrightarrow5x-10\sqrt{x}=2x-6\sqrt{x}\)
\(\Leftrightarrow3x-4\sqrt{x}=0\)
\(\Leftrightarrow\sqrt{x}\left(3\sqrt{x}-4\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\\sqrt{x}=\dfrac{4}{3}\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=0\left(tm\right)\\x=\dfrac{16}{9}\left(tm\right)\end{matrix}\right.\)
