`-` 23)

`a)`

`B = (sqrt(x))/(sqrt(x) - 1) - (2*sqrt(x))/(x - 1)`

`= (sqrt(x)*(sqrt(x) + 1))/(x - 1) - (2*sqrt(x))/(x - 1)`

`= (x + sqrt(x) - 2*sqrt(x))/(x - 1)`

`= (x - sqrt(x))/(x - 1)`

`= (sqrt(x)*(sqrt(x) - 1))/((sqrt(x) - 1)*(sqrt(x) + 1))`

` = sqrt(x)/(sqrt(x) + 1)`

`C = (sqrt(x))/(sqrt(x) + 1) - 1/(x + sqrt(x))`

`= (sqrt(x))/(sqrt(x) + 1) - 1/(sqrt(x)*(sqrt(x) + 1))`

`= (x - 1)/(sqrt(x)*(sqrt(x) + 1))`

`= ((sqrt(x) - 1)*(sqrt(x) + 1))/(sqrt(x)*(sqrt(x) + 1))`

`= (sqrt(x) - 1)/sqrt(x)`

 `b)`

Có: `BC = (sqrt(x))/(sqrt(x) + 1) * (sqrt(x) - 1)/sqrt(x)`

`= (sqrt(x) - 1)/(sqrt(x) + 1)=1/3`  

`<=>3*(sqrt(x) - 1) = sqrt(x) + 1`

`<=> 3*sqrt(x) - 3 = sqrt(x) + 1`

`<=> 2*sqrt(x) = 4`

`<=> sqrt(x) = 2`

`<=>x = 4`

 `c)`

`B.C= \frac{\sqrt{x} - 1}{\sqrt{x} + 1} = \frac{\sqrt{x} + 1 - 2}{\sqrt{x} + 1} = 1 - \frac{2}{\sqrt{x} + 1}`

Có `x>0` và $x\neq1$ `=>sqrt{x}>0` và `sqrt{x}`$\neq1$

`=>0 < \frac{2}{\sqrt{x} + 1} < 2`

`=>-1 < -\frac{2}{\sqrt{x} + 1} < 0`

`=>0 < 1 - \frac{2}{\sqrt{x} + 1} < 1`

Vậy B.C không thể nhận giá trị nguyên.