a: \(P=\dfrac{4\sqrt{x}-6-\sqrt{x}+1}{2\sqrt{x}-3}:\dfrac{6\sqrt{x}+1+\sqrt{x}\left(2\sqrt{x}-3\right)}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3\sqrt{x}-5}{2\sqrt{x}-3}\cdot\dfrac{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}{6\sqrt{x}+1+2x-3\sqrt{x}}\)
\(=\dfrac{3\sqrt{x}-5}{2x+3\sqrt{x}+1}\cdot\left(\sqrt{x}+1\right)=\dfrac{3\sqrt{x}-5}{2\sqrt{x}+1}\)
b: Khi x=(3-2căn 2)/4 thì \(P=\left[3\cdot\dfrac{\sqrt{2}-1}{2}-5\right]:\left[2\cdot\dfrac{\sqrt{2}-1}{2}+1\right]\)
\(=\left(\dfrac{3}{2}\sqrt{2}-\dfrac{3}{2}-5\right):\left(\sqrt{2}\right)\)
\(=\dfrac{3\sqrt{2}-13}{2}\cdot\dfrac{1}{\sqrt{2}}=\dfrac{3\sqrt{2}-13}{2\sqrt{2}}=\dfrac{6-13\sqrt{2}}{4}\)
