a: \(\frac{6\sqrt{x}}{2\sqrt{x}-1}-\frac{4\sqrt{x}}{12x+4\sqrt{x}}-\frac{36x+2\sqrt{x}+1}{12x-2\sqrt{x}-2}\)
\(=\frac{6\sqrt{x}}{2\sqrt{x}-1}-\frac{4\sqrt{x}}{4\sqrt{x}\left(3\sqrt{x}+1\right)}-\frac{36x+2\sqrt{x}+1}{2\left(6x-\sqrt{x}-1\right)}\)
\(=\frac{6\sqrt{x}}{2\sqrt{x}-1}-\frac{1}{3\sqrt{x}+1}-\frac{36x+2\sqrt{x}+1}{2\left(6x-3\sqrt{x}+2\sqrt{x}-1\right)}\)
\(=\frac{6\sqrt{x}}{2\sqrt{x}-1}-\frac{1}{3\sqrt{x}+1}-\frac{36x+2\sqrt{x}+1}{2\left(2\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}\)
\(=\frac{12\sqrt{x}\left(3\sqrt{x}+1\right)-2\left(2\sqrt{x}-1\right)-36x-2\sqrt{x}-1}{2\left(2\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}\)
\(=\frac{36x+12\sqrt{x}-4\sqrt{x}+2-36x-2\sqrt{x}-1}{2\left(2\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}=\frac{6\sqrt{x}+1}{2\left(2\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}\)
Ta có: \(P=\left(\frac{6\sqrt{x}}{2\sqrt{x}-1}-\frac{4\sqrt{x}}{12x+4\sqrt{x}}-\frac{36x+2\sqrt{x}+1}{12x-2\sqrt{x}-2}\right):\frac{6\sqrt{x}+1}{28x-14\sqrt{x}}\)
\(=\frac{6\sqrt{x}+1}{2\left(2\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}\cdot\frac{28x-14\sqrt{x}}{6\sqrt{x}+1}=\frac{14\sqrt{x}\left(2\sqrt{x}-1\right)}{2\left(2\sqrt{x}-1\right)\left(3\sqrt{x}+1\right)}=\frac{7\sqrt{x}}{3\sqrt{x}+1}\)
