`ĐKXĐ:x\ge0,x\ne1`
`P=({x+2}/{x\sqrt{x}-1}+{\sqrt{x}}/{x+\sqrt{x}+1}+{1}/{1-\sqrt{x}}):{\sqrt{x}-1}/{2}`
`=[{x+2}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}+{\sqrt{x}}/{x+\sqrt{x}+1}-{1}/{\sqrt{x}-1}]:{\sqrt{x}-1}/{2}`
`=[{x+2}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}+{\sqrt{x}(\sqrt{x}-1)}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}-{x+\sqrt{x}+1}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}]:{\sqrt{x}-1}/{2}`
`={x+2+\sqrt{x}(\sqrt{x}-1)-(x+\sqrt{x}+1)}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}:{\sqrt{x}-1}/{2}`
`={x+2+x-\sqrt{x}-x-\sqrt{x}-1}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}:{\sqrt{x}-1}/{2}`
`={x-2\sqrt{x}+1}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}.{2}/{\sqrt{x}-1}`
`={(\sqrt{x}-1)^2}/{(\sqrt{x}-1)(x+\sqrt{x}+1)}.{2}/{\sqrt{x}-1}`
`={2}/{x+\sqrt{x}+1}`
Vậy với `x\ge0,x\ne1` thì `P={2}/{x+\sqrt{x}+1}`
