Bài 2;
a: \(P=\left(\frac{3}{\sqrt{x}-2}+\frac{\sqrt{x}-6}{x-4}\right):\left(1+\frac{3}{x-4}\right)\)
\(=\left(\frac{3}{\sqrt{x}-2}+\frac{\sqrt{x}-6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\right):\frac{x-4+3}{x-4}\)
\(=\frac{3\left(\sqrt{x}+2\right)+\sqrt{x}-6}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\cdot\frac{x-4}{x-1}\)
\(=\frac{4\sqrt{x}}{x-1}\)
b: \(Q=\left(\frac{\sqrt{x}}{\sqrt{x}-2}+\frac{2}{x-2\sqrt{x}}\right):\left(\frac{2}{\sqrt{x}-2}+1\right)\)
\(=\left(\frac{\sqrt{x}}{\sqrt{x}-2}+\frac{2}{\sqrt{x}\left(\sqrt{x}-2\right)}\right):\frac{2+\sqrt{x}-2}{\sqrt{x}-2}\)
\(=\frac{x+2}{\sqrt{x}\left(\sqrt{x}-2\right)}\cdot\frac{\sqrt{x}-2}{\sqrt{x}}=\frac{x+2}{x}\)
c: \(L=\left(\frac{3\sqrt{x}-6}{x-4}-\frac{1}{\sqrt{x}-3}\right):\left(\frac{5}{\sqrt{x}-3}-2\right)\)
\(=\left(\frac{3\left(\sqrt{x}-2\right)}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{1}{\sqrt{x}-3}\right):\frac{5-2\left(\sqrt{x}-3\right)}{\sqrt{x}-3}\)
\(=\left(\frac{3}{\sqrt{x}+2}-\frac{1}{\sqrt{x}-3}\right):\frac{5-2\sqrt{x}+6}{\sqrt{x}-3}\)
\(=\frac{3\left(\sqrt{x}-3\right)-\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(\sqrt{x}-3\right)}\cdot\frac{\sqrt{x}-3}{-2\sqrt{x}+11}\)
\(=\frac{3\sqrt{x}-9-\sqrt{x}-2}{\left(\sqrt{x}+2\right)\left(-2\sqrt{x}+11\right)}=\frac{2\sqrt{x}-11}{-\left(\sqrt{x}+2\right)\left(2\sqrt{x}-11\right)}=\frac{-1}{\sqrt{x}+2_{}}\)
d: \(X=\left(\frac{\sqrt{x}-4}{x-2\sqrt{x}}+\frac{3}{\sqrt{x}-2}\right):\left(\frac{\sqrt{x}+2}{\sqrt{x}}-\frac{\sqrt{x}}{\sqrt{x}-2}\right)\)
\(=\frac{\sqrt{x}-4+3\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}:\frac{\left(\sqrt{x}+2\right)\left(\sqrt{x}-2\right)-x}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\frac{4\sqrt{x}-4}{\sqrt{x}\left(\sqrt{x}-2\right)}\cdot\frac{\sqrt{x}\left(\sqrt{x}-2\right)}{x-4-x}\)
\(=\frac{4\left(\sqrt{x}-1\right)}{-4}=-\sqrt{x}+1\)
e: \(E=\left(\frac{1}{\sqrt{x}+1}-\frac{2\sqrt{x}-2}{x\sqrt{x}-\sqrt{x}+x-1}\right):\left(\frac{1}{\sqrt{x}-1}-\frac{2}{x-1}\right)\)
\(=\left(\frac{1}{\sqrt{x}+1}-\frac{2\left(\sqrt{x}-1\right)}{\left(x-1\right)\left(\sqrt{x}+1\right)}\right):\frac{\sqrt{x}+1-2}{x-1}\)
\(=\left(\frac{1}{\sqrt{x}+1}-\frac{2}{\left(\sqrt{x}+1\right)^2}\right):\frac{\sqrt{x}-1}{x-1}\)
\(=\frac{\sqrt{x}+1-2}{\left(\sqrt{x}+1\right)^2}\cdot\left(\sqrt{x}+1\right)=\frac{\sqrt{x}-1}{\sqrt{x}+1}\)
f: \(F=\left(\frac{1}{x-4}-\frac{1}{x-4\sqrt{x}+4}\right):\frac{\sqrt{x}}{x-2\sqrt{x}}\)
\(=\left(\frac{1}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}-\frac{1}{\left(\sqrt{x}-2\right)^2}\right):\frac{\sqrt{x}}{\sqrt{x}\left(\sqrt{x}-2\right)}\)
\(=\frac{\sqrt{x}-2-\sqrt{x}-2}{\left(\sqrt{x}-2\right)^2\cdot\left(\sqrt{x}+2\right)}\cdot\left(\sqrt{x}-2\right)=\frac{-4}{\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}\)
\(=\frac{-4}{x-4}\)
