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=\(\frac{2x+3\sqrt{x}-6\sqrt{2}}{\left(\sqrt{x}-1\right)\left(\sqrt{x}+2\right)}\)
