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A=\(\frac{3x+\sqrt{9x}-3}{x+\sqrt{x}-2}-\frac{\sqrt{x}+1}{\sqrt{x}+2}+\frac{\sqrt{2}+2}{1-\sqrt{x}}\)
=\(\frac{3x+\sqrt{9}-3}{\sqrt{x}.\sqrt{x}+\sqrt{2x}-\sqrt{x}-2}-\frac{\sqrt{x}+1}{\sqrt{x}+2}-\frac{\sqrt{2+2}}{\sqrt{x}-1}\) ( ở phân số đầu là \(\sqrt{9x}nhe\) )
=\(\frac{3x+\sqrt{9x}-3}{\sqrt{x}\left(\sqrt{x}-1\right)+2\left(\sqrt{x}-1\right)}-\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}-\frac{\left(\sqrt{2}+2\right)\left(\sqrt{2}+2\right)}{\left(\sqrt{2}+2\right)\left(\sqrt{x}-1\right)}\)
=\(\frac{3x+\sqrt{9x}-3-\left(x-1\right)-\left(2+4\sqrt{2}+4\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
=\(\frac{2x+3\sqrt{x}-2\sqrt{2}-4\sqrt{2}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
=\(\frac{2x+3\sqrt{x}-6\sqrt{2}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
Vậy A=\(\frac{2x+3\sqrt{x}-6\sqrt{2}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(P=\frac{3x+3\sqrt{x}-3-\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)-\left(\sqrt{x}-2\right)\left(\sqrt{x}+2\right)}{x+\sqrt{x}-2}\)
\(P=\frac{3x+3\sqrt{x}-3-x+1-x+4}{x+\sqrt{x}-2}\)
\(P=\frac{x+3\sqrt{x}+2}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
\(P=\frac{\left(\sqrt{x}+1\right)\left(\sqrt{x}+2\right)}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}=\frac{\sqrt{x}+1}{\sqrt{x}-1}\)
\(Q=\frac{3x+\sqrt{9x}-3}{x+\sqrt{x}-2}-\frac{\sqrt{x}+1}{\sqrt{x}+2}+\frac{\sqrt{x}-2}{1-\sqrt{x}}\)ĐK : \(x\ge0;x\ne1\)
\(=\frac{3x+3\sqrt{x}-3-\left(1-x\right)+x-4}{\left(\sqrt{x}+2\right)\left(1-\sqrt{x}\right)}=\frac{5x+3\sqrt{x}-8}{\left(\sqrt{x}+2\right)\left(1-\sqrt{x}\right)}=\frac{-8-5\sqrt{x}}{\sqrt{x}+2}\)