a: Ta có: \(P=\dfrac{3\sqrt{x}+2}{\sqrt{x}+1}-\dfrac{2\sqrt{x}-3}{3-\sqrt{x}}-\dfrac{3\left(3\sqrt{x}-5\right)}{x-2\sqrt{x}-3}\)
\(=\dfrac{\left(3\sqrt{x}+2\right)\left(\sqrt{x}-3\right)+\left(2\sqrt{x}-3\right)\left(\sqrt{x}+1\right)-3\left(3\sqrt{x}-5\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{3x-7\sqrt{x}-6+2x-\sqrt{x}-3-9\sqrt{x}+15}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{5x-17\sqrt{x}+6}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{5x-15\sqrt{x}-2\sqrt{x}+6}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+1\right)}\)
\(=\dfrac{5\sqrt{x}-2}{\sqrt{x}+1}\)
b: Thay \(x=4+2\sqrt{3}\) vào P, ta được:
\(P=\dfrac{5\left(\sqrt{3}+1\right)-2}{2+\sqrt{3}}=-9+7\sqrt{3}\)