Đáp án:
Giải thích các bước giải:
`a)`
ĐKXĐ : `x \ge 0 , x \ne 9`
`B = ((x+3)/(x-9)+1/(sqrtx+3))\div sqrtx/(sqrtx-3)`
`= ((x+3)/((sqrtx-3)(sqrtx+3)) + 1/(sqrtx+3))*(sqrtx-3)/sqrtx`
`= (x+3+sqrtx-3)/((sqrtx-3)(sqrtx+3)) * (sqrtx-3)/(sqrtx)`
`= (x+sqrtx)/((sqrtx-3)(sqrtx+3)) * (sqrtx-3)/(sqrtx)`
`= (x+sqrtx)/((sqrtx+3)sqrtx)`
`= (x+sqrtx)/(x+3sqrtx)`
`= ((x+sqrtx)(x-3sqrtx))/(x^2-9x)`
`= (sqrtx(sqrtx+1)sqrtx(sqrtx-3))/(x(sqrtx-3)(sqrtx+3))`
`= (sqrtx(sqrtx+1)sqrtx)/(x(sqrtx+3))`
`= (sqrtx+1)/(sqrtx+3)`
`b)`
`B - 1/3`
`= (sqrtx+1)/(sqrtx+3) - 1/3`
`= (3(sqrtx+1)-(sqrtx+3))/(3(sqrtx+3))`
`= (3sqrtx+3-sqrtx-3)/(3sqrtx+9)`
`= (2sqrtx)/(3sqrtx+9) > 0`
`-> B > 1/3`
`->` đpcm
