Đáp án:

`a.`

`B=x/(x-1)+3/(x+1)-(6x-4)/(x^(2)-1)`    (ĐKXĐ : `x \ne +-1`)

`=[x(x+1)]/[(x-1)(x+1)]+[3(x-1)]/[(x+1)(x-1)]-(6x-4)/[(x+1)(x-1)]`

`=(x^(2)+x+3x-3-6x+4)/[(x+1)(x-1)]`

`=(x^(2)-2x+1)/[(x+1)(x-1)]`

 `=(x-1)^(2)/[(x+1)(x-1)]`

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

`b.`

Để `B=5`

`⇔(x-1)/(x+1)=5`     (ĐK : `x \ne +-1`)

`⇔5(x+1)=x-1`

`⇔5x+5=x-1`

`⇔5x-x=-1-5`

`⇔4x=-6`

`⇔x=-3/2`    (Thỏa mãn ĐKXĐ)

Vậy `x=-3/2` thì `B=5`

Đáp án+Giải thích các bước giải:

a)

`B=\frac{x}{x-1}+\frac{3}{x+1}-\frac{6x-4}{x^2-1}`
ĐKXĐ: `xne+-1`
`=\frac{x}{x-1}+\frac{3}{x+1}-\frac{6x-4}{(x-1)(x+1)}`
`=\frac{x(x+1)+3(x-1)-(6x-4)}{(x-1)(x+1)}`
`=\frac{x^2+x+3x-3-6x+4}{(x-1)(x+1)}`
`=\frac{x^2-2x+1}{(x-1)(x+1)}`
`=\frac{(x-1)^2}{(x-1)(x+1)}`
`=\frac{x-1}{x+1}`

Vậy `B=\frac{x-1}{x+1}` với `xne+-1`

b)

Ta có: `B=5`

`<=>\frac{x-1}{x+1}=5` 

`<=>\frac{x-1}{x+1}-5=0` 

`<=>\frac{x-1-5(x+1)}{x+1}=0` 

`<=>\frac{x-1-5x-5}{x+1}=0` 

`<=>\frac{-4x-6}{x+1}=0` 

`=>-4x-6=0`

`<=>-4x=6`

`<=>x=-3/2(N)`

Vậy `x=-3/2` để `B=5`