a: ĐKXĐ: \(\left\{{}\begin{matrix}x>=0\\x< >1\\x< >4\end{matrix}\right.\)
b: \(A=\dfrac{\left(\sqrt{x}-3\right)}{\sqrt{x}-2}-\dfrac{2\sqrt{x}-1}{\sqrt{x}-1}+\dfrac{x-2}{x-3\sqrt{x}+2}\)
\(=\dfrac{\left(\sqrt{x}-3\right)\left(\sqrt{x}-1\right)-\left(2\sqrt{x}-1\right)\left(\sqrt{x}-2\right)+x-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{x-4\sqrt{x}+3-2x+4\sqrt{x}+\sqrt{x}-2+x-2}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}\)
\(=\dfrac{\sqrt{x}-1}{\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)}=\dfrac{1}{\sqrt{x}-2}\)
c: A nguyên khi \(\sqrt{x}-2\in\left\{1;-1\right\}\)
=>\(\sqrt{x}\in\left\{3;1\right\}\)
Kết hợp ĐKXĐ, ta được: \(\sqrt{x}=3\)
=>x=9
