`ĐKXĐ:x\ge0,x\ne1`
`F=({1}/{\sqrt{x}-1}-{1}/{x\sqrt{x}-1}).{3\sqrt{x}-3}/{x+\sqrt{x}}`
`=[{1}/{\sqrt{x}-1}-{1}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}].{3(\sqrt{x}-1)}/{x+\sqrt{x}}`
`=[{x+\sqrt{x}+1}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}-{1}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}].{3(\sqrt{x}-1)}/{x+\sqrt{x}}`
`={x+\sqrt{x}+1-1}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}.{3(\sqrt{x}-1)}/{x+\sqrt{x}}`
`={x+\sqrt{x}}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}.{3(\sqrt{x}-1)}/{x+\sqrt{x}}`
`={3}/{x+\sqrt{x}+1}`
Vậy với `x\ge0,x\ne1` thì `F={3}/{x+\sqrt{x}+1}`