`((2\sqrt{x}+x)/(x\sqrt{x}-1)-1/(\sqrt{x}-1))÷(1-(\sqrt{x}+2)/(x\sqrt{x}+1)) (đk:x\ne0;x\ne≥0)`

`=[(2\sqrt{x}+x)/((\sqrt{x}-1)(x+\sqrt{x}+1))-1/(\sqrt{x}-1)]÷(x\sqrt{x}+1-\sqrt{x}-2)/(x\sqrt{x}+1)`

`=(2\sqrt{x}+x-(x+\sqrt{x}+1))/((\sqrt{x}-1)(x+\sqrt{x}+1))÷(x\sqrt{x}-\sqrt{x}-1)/(x\sqrt{x}+1)`

`=(2\sqrt{x}+x-x-\sqrt{x}-1)/((\sqrt{x}-1)(x+\sqrt{x}+1))·(x\sqrt{x}+1)/(x\sqrt{x}-\sqrt{x}-1)`

`=(\sqrt{x}-1)/((\sqrt{x}-1)(x+\sqrt{x}+1))·(x\sqrt{x}+1)/(x\sqrt{x}-\sqrt{x}-1)`

`=1/(x+\sqrt{x}+1)·(x\sqrt{x}+1)/(x\sqrt{x}-\sqrt{x}-1)`

`=(x\sqrt{x}+1)/((x+\sqrt{x}+1)(x\sqrt{x}-\sqrt{x}-1))`