$Q=\Bigg(\dfrac{\sqrt{x}+2}{x+2\sqrt{x}+1}-\dfrac{\sqrt{x}-2}{x-1}\Bigg).\dfrac{\sqrt{x}+1}{\sqrt{x}}\,\,\,(x>0;\,x\ne 1;\, x\ne 2)\\=\Bigg[\dfrac{\sqrt{x}+2}{(\sqrt{x}+1)^2}-\dfrac{\sqrt{x}-2}{(\sqrt{x}-1)(\sqrt{x}+1)}\Bigg].\dfrac{\sqrt{x}+1}{\sqrt{x}}\\=\dfrac{(\sqrt{x}+2)(\sqrt{x}-1)-(\sqrt{x}-2)(\sqrt{x}+1)}{(\sqrt{x}-1)(\sqrt{x}+1)^2}.\dfrac{\sqrt{x}+1}{\sqrt{x}}\\=\dfrac{x+\sqrt{x}-2-(x-\sqrt{x}-2)}{(\sqrt{x}-1)(\sqrt{x}+1)}.\dfrac{1}{\sqrt{x}}\\=\dfrac{2\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}.\dfrac{1}{\sqrt{x}}\\=\dfrac{2}{x-1}$
