Đáp án:

 Giải thích các bước giải:

 a)

`2x-1=4x+2`

`<=>2x-4x=2+1`

`<=>-2x=3`

`<=>x=-3/2`

Vậy, `S={-3/2}`

b)

`(5-x)/3-x=(2x-4)/6`

`<=>[2(5-x)]/6-(6x)/6=(2x-4)/6`

`<=>2(5-x)-6x=2x-4`

`<=>10-2x-6x=2x-4`

`<=>-2x-6x-2x=-4-10`

`<=>-10x=-14`

`<=>x=7/5`

Vậy, `S={7/5}`

C)

`(x-2)(x+1)+(x-2)(x+3)=0`

`<=>(x-2)(x+1+x+3)=0`

`<=>(x-2)(2x+4)=0`

`<=>`\(\left[ \begin{array}{l}x-2=0\\2x+4=0\end{array} \right.\)

`<=>`\(\left[ \begin{array}{l}x=2\\x=-2\end{array} \right.\) 

Vậy, `S={+-2}`

D)

ĐKXĐ: $x\neq1;x\neq3$

`(x-5)/(x-1)-3/(x-3)=1`

`<=>[(x-5)(x-3)]/[(x-1)(x-3)]-[3(x-1)]/[(x-1)(x-3)]=[(x-1)(x-3)]/[(x-1)(x-3)]`

`=>(x-5)(x-3)-3(x-1)=(x-1)(x-3)`

`<=>x^2-3x-5x+15-3x+3=x^2-3x-x+3`

`<=>x^2-3x-5x-3x-x^2+3x+x=3-15`

`<=>-7x=-12`

`<=>x=12/7`( TM)

Vậy, `S={12/7}`

`#water`

`a)2x-1=4x+2`

`<=>2x-4x=2+1`

`<=>-2=3`

`<=>x=-3/2`

Vậy S = `{-3/2}`

`b)(5-x)/3-x=(2x-4)/6`

`<=>(5-x)/3-x=(2(x−2))/6`

`<=>(5-x)/3-x=(x−2)/6`

`=>5−x−3x=x−2`

`<=>5-4x=x-2`

`<=>4x-x=2-5`

`<=>-5x=-7`

`<=>x=\frac{7}{5}`

Vậy S = `{7/5}`

`c)(x-2)(x+1)+(x-2)(x+3)=0`

`<=>(x−2)(x+1+x+3)=0`

TH1: `x-2=0`

`<=>x=2`

TH2: `x+1+x+3=0`

`<=>2x+4=0`

`<=>2x=-4`

`<=>x=-2`

Vậy S = `{+-2}`

`d)(x-5)/(x-1)-3/(x-3)=1`

ĐKXĐ: `x!=1;x!=3`

`<=>(x−5)(x−3)−3(x−1)=(x−1)(x−3)`

`<=>x^2-11x+18=x^2-4x+3`

`<=>−11x+18=−4x+3`

`<=>-4x+11x+3=18`

`<=>7x+3=18`

`<=>7x=18-3`

`<=>7x=15`

`<=>x=\frac{15}{7}(tm)`

Vậy S = `{15/7}`