\(M=\left(\dfrac{2x+1}{x\sqrt{x}-1}-\dfrac{1}{\sqrt{x}-1}\right):\left(1-\dfrac{x+4}{x+\sqrt{x}+1}\right)=\dfrac{2x+1-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}:\dfrac{x+\sqrt{x}+1-x-4}{x+\sqrt{x}+1}=\dfrac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}.\dfrac{x+\sqrt{x}+1}{\sqrt{x}-3}=\dfrac{\sqrt{x}}{\sqrt{x}-3}\left(x\ge0;x\ne1;x\ne9\right)\)
Lời giải:
\(M=\left(\frac{2x+1}{(\sqrt{x}-1)(x+\sqrt{x}+1)}-\frac{x+\sqrt{x}+1}{(\sqrt{x}-1)(x+\sqrt{x}+1)}\right):\frac{x+\sqrt{x}+1-(x+4)}{x+\sqrt{x}+1}\)
\(=\frac{2x+1-(x+\sqrt{x}+1)}{(\sqrt{x}-1)(x+\sqrt{x}+1)}:\frac{\sqrt{x}-3}{x+\sqrt{x}+1}\)
\(=\frac{x-\sqrt{x}}{(\sqrt{x}-1)(x+\sqrt{x}+1)}.\frac{x+\sqrt{x}+1}{\sqrt{x}-3}\)
\(=\frac{\sqrt{x}(\sqrt{x}-1)(x+\sqrt{x}+1)}{(\sqrt{x}-1)(x+\sqrt{x}+1)(\sqrt{x}-3)}\)
\(=\frac{\sqrt{x}}{\sqrt{x}-3}\)
