Đáp án:

Giải thích các bước giải:

 `4x-8=0`

`4x=8`

`x=2`

;

;

`3x^2-x=0`

`x(3x-1)=0`

`=>x=0;x=-1/3`

;

;

Xét `x<8`.

$8-x=2x-1$

$-x=2x-9$

$x=3$

Xét `x>=8`

`x-8=2x-1`

`x-8-2x+1=0`

`-x-7=0`

`x=-7` Loại

;

;

Quy đồng lên:

`5(x+3) +4(x-3)=x-5`

`5x+15 + 4x-12-x+5=0`

`8x+8=0`

`x=-1`

`1)`

`a)4x-8=0`

`⇔4x=8`

`⇔x=8:4`

`⇔x=2`

Vậy `S={2}`

`b)3x²-x=0`

`⇔x(3x-1)=0`

`(1)x=0`

`(2)3x-1=0⇔x=1/3`

Vậy `S={0;1/3}`

`c)5/(x-3)+4/(x+3)=(x-5)/(x²-9)(ĐKXĐ:x`$\neq$ `±3)`

`⇔5/(x-3)+4/(x+3)=(x-5)/[(x+3)(x-3)]`

`⇔[5(x+3)]/[(x+3)(x-3)]+[4(x-3)]/[(x+3)(x-3)]=(x-5)/[(x+3)(x-3)]`

`⇒5(x+3)+4(x-3)=x-5`

`⇔5x+15+4x-12=x-5`

`⇔9x+3=x-5`

`⇔9x-x=-5-3`

`⇔8x=-8`

`⇔x=-1(TM` `ĐKXĐ)`

Vậy `S={-1}`

`d)|x-8|=2x-1`

    `|x-8|=x-8` nếu `x≥8` 

             `8-x` nếu `x<8`

*Nếu `x≥8` ta có:

    `x-8=2x-1`

`⇔x-2x=-1+8`

`⇔-x=7`

`⇔x=-7(loại)`

*Nếu `x<8` ta có:

    `8-x=2x-1`

`⇔-x-2x=-1-8`

`⇔-3x=-9`

`⇔x=3(TM)`

Vậy `S={3}`