`1)M=(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{x-1}):(\frac{\sqrt{x}}{\sqrt{x}-1}-1)(x>=0;x\ne1)`
`=(\frac{\sqrt{x}+1+\sqrt{x}}{(\sqrt{x}-1)(\sqrt{x}+1)}):(\frac{\sqrt{x}-\sqrt{x}+1}{\sqrt{x}-1})`
`=\frac{2\sqrt{x}+1}{(\sqrt{x}-1)(\sqrt{x}+1)}.(\sqrt{x}-1)`
`=\frac{2\sqrt{x}+1}{\sqrt{x}+1}`
Vậy `M=\frac{2\sqrt{x}+1}{\sqrt{x}+1}`
`2)`Với `M<3/2`
`=>\frac{2\sqrt{x}+1}{\sqrt{x}+1}<3/2`
`<=>\frac{4\sqrt{x}+2-3(\sqrt{x}+1)}{2(\sqrt{x}+1)}<0`
`<=>\frac{4\sqrt{x}+2-3\sqrt{x}-3}{2\sqrt{x}+2}<0`
`<=>\frac{\sqrt{x}-1}{2\sqrt{x}+2}<0`
Vì `2\sqrt{x}+2>0`
`<=>\sqrt{x}-1<0`
`<=>\sqrt{x}<1<=>x<1`
Kết hợp cùng ĐKXĐ
Vậy `0<=x<1` thì `M<3/2`
