Đáp án+Giải thích các bước giải:
`a)ĐKXĐ:{(x>=0),(sqrtx-1 ne 0),(x-sqrtx ne 0),(x-1 ne 0):}`
`<=>{(x>0),(x ne 1)`
`b)P=(sqrtx/(sqrtx-1)-1/(x-sqrtx)):(1/(sqrtx+1)+2/(x-1))`
`P=(x/(sqrtx(sqrtx-1))-1/(sqrtx(sqrtx-1))):((sqrtx-1)/((sqrtx-1)(sqrtx+1))+2/((sqrtx-1)(sqrtx+1)))`
`P=(x-1)/(sqrtx(sqrtx-1)):(sqrtx+1)/(x-1)`
`P=(x-1)^2/(sqrtx(x-1))`
`P=(x-1)/sqrtx`
`c)P<0`
Mà `sqrtx>0`
`<=>x-1<0`
`<=>x<1`
`<=>0<x<1`
`5)Q=1/(x-2sqrtx+3)`
`Q=1/(x-2sqrtx+1+2)`
`Q=1/((sqrtx-1)^2+2)`
Vì `(sqrtx-1)^2>=0`
`=>(sqrtx-1)^2+2>=2>0`
`=>1/((sqrtx-1)^2+2)<=1/2`
Hay `Q<=1/2`
Dấu "=" xảy ra khi `sqrtx=1<=>x=1.`