`P=(4x+3)/(sqrtx-1)`
`Q=(2sqrtx-1)/(sqrtx+1)+(5sqrtx-1)/(x-1)`
`a)x=1/4`
`=>sqrtx=1/2`
`=>P=(1+3)/(1/2-1)=4/(-1/2)=-8`
`b)Q=((2sqrtx-1)(sqrtx-1)+5sqrtx-1)/(x-1)`
`=(2x-3sqrtx+1+5sqrtx-1)/(x-1)`
`=(2x+2sqrtx)/(x-1)`
`=(2sqrtx(sqrtx+1))/((sqrtx-1)(sqrtx+1))`
`=(2sqrtx)/(sqrtx-1)`
`c)S=P/Q`
`=(4x+3)/(sqrtx-1).(sqrtx-1)/(2sqrtx)`
`=(4x+3)/(2sqrtx)`
`=2sqrtx+3/(2sqrtx)`
Áp dụng BĐT cosi với 2 số dương.
`=>2sqrtx+3/(2sqrtx)>=2sqrt3`
Dấu "=' xảy ra khi `2sqrtx=3/(2sqrtx)<=>4x=3<=>x=3/4`