a: \(P=\dfrac{4\sqrt{x}-6-\sqrt{x}+1}{2\sqrt{x}-3}:\left(\dfrac{6\sqrt{x}+1}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}+\dfrac{\sqrt{x}}{\sqrt{x}+1}\right)\)
\(=\dfrac{3\sqrt{x}-5}{2\sqrt{x}-3}:\dfrac{6\sqrt{x}+1+2x-3\sqrt{x}}{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3\sqrt{x}-5}{2\sqrt{x}-3}\cdot\dfrac{\left(2\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}{2x+3\sqrt{x}+1}\)
\(=\dfrac{3\sqrt{x}-5}{2\sqrt{x}+1}\)
b: Thay \(x=\dfrac{3-2\sqrt{2}}{4}\) vào P, ta được:
\(P=\left(3\cdot\dfrac{\sqrt{2}-1}{2}-5\right):\left(2\cdot\dfrac{\sqrt{2}-1}{2}+1\right)\)
\(=\dfrac{3\sqrt{2}-3-10}{2}:\sqrt{2}\)
\(=\dfrac{3\sqrt{2}-13}{2\sqrt{2}}=\dfrac{6-13\sqrt{2}}{4}\)