ĐKXĐ: \(x\ne 1;x\ge 0\)
\(\dfrac{2\sqrt x}{\sqrt x+1}-\dfrac{\sqrt x+2}{\sqrt x-1}+\dfrac{2\sqrt x+3}{x-1}\\=\dfrac{2\sqrt x(\sqrt x-1)}{(\sqrt x-1)(\sqrt x+1)}-\dfrac{(\sqrt x+2)(\sqrt x+1)}{(\sqrt x-1)(\sqrt x+1)}+\dfrac{2\sqrt x+3}{(\sqrt x-1)(\sqrt x+1)}\\=\dfrac{2x-2\sqrt x-x-3\sqrt x-2+2\sqrt x+4}{(\sqrt x-1)(\sqrt x+1)}\\=\dfrac{x-3\sqrt x+2}{(\sqrt x-1)(\sqrt x+1)}\\=\dfrac{x-2\sqrt x-\sqrt x+2}{(\sqrt x-1)(\sqrt x+1)}\\=\dfrac{\sqrt x(\sqrt x-2)-(\sqrt x-2)}{(\sqrt x+1)(\sqrt x-1)}\\=\dfrac{(\sqrt x-1)(\sqrt x-2)}{(\sqrt x+1)(\sqrt x-1)}\\=\dfrac{\sqrt x-2}{\sqrt x+1}\)
