~ Tham khảo :
Câu `a)` :
`A = ((xsqrtx+x+sqrtx)/(xsqrtx-1)-(sqrtx+5)/(1-sqrtx)) * (x-1)/(3x+2sqrtx-1)`
`= ((sqrtx(x+sqrtx+1))/((sqrtx-1)(x+sqrtx+1))-(sqrtx+5)/(-(sqrtx-1)))*((sqrtx-1)(sqrtx+1))/(3x+3sqrtx-sqrtx-1)`
`= (sqrtx/(sqrtx-1)+(sqrtx+5)/(sqrtx-1)) * ((sqrtx-1)(sqrtx+1))/(3sqrtx(sqrtx+1)-(sqrtx+1))`
`= (sqrtx+sqrtx+5)/(sqrtx-1) *((sqrtx-1)(sqrtx+1))/((sqrtx+1)(3sqrtx-1))`
`= (2sqrtx+5) * 1/(3sqrtx-1)`
`= (2sqrtx+5)/(3sqrtx-1)`
Câu `b)` :
Ta có : `A = (2sqrtx+5)/(3sqrtx-1)`
`⇒ A > 0`
`⇔ (2sqrtx+5)/(3sqrtx-1) > 0`
`⇔ 3sqrtx - 1 > 0`
`⇔ 3sqrtx > 1`
`⇔ sqrtx > 1/3`
`⇔ (sqrtx)^2 > (1/3)^2`
`⇔ x > 1/9`
Vậy khi `x > 1/9` sẽ thỏa mãn đề bài .
