Giải hộ mk đến câu 6 aj hứa sẽ vote 5sao mk đang cần gấp

Đáp án+Giải thích các bước giải:

 `1)`

`\frac{x+2}{x-2}-5/x=\frac{8}{x^{2}-2x}`

`(đk:x\ne0;x\ne2)`

`<=>\frac{x.(x+2)}{x.(x-2)}-\frac{5.(x-2)}{x.(x-2)}=\frac{8}{x.(x-2)}`

`=>x.(x+2)-5.(x-2)=8`

`<=>x^{2}+2x-5x+10=8`

`<=>x^{2}-3x+10-8=0`

`<=>x^{2}-x-2x+2=0`

`<=>x.(x-1)-2.(x-1)=0`

`<=>(x-1).(x-2)=0`

`<=>x-1=0` hoặc `x-2=0`

`<=>x=1(tmđk)` hoặc `x=2(ktmđk)`

`<=>x=1`

Vậy `S={1}.`

`2)`

`\frac{x-1}{x}+\frac{1}{x+1}=\frac{2x+1}{x^{2}+x}`

`(đk:x\ne0;x\ne-1)`

`<=>\frac{(x-1).(x+1)}{x.(x+1)}+\frac{x}{x.(x+1)}=\frac{2x+1}{x.(x+1)}`

`=>x^{2}-1^{2}+x=2x+1`

`<=>x^{2}+x-1-2x-1=0`

`<=>x^{2}-x-2=0`

`<=>x^{2}-2x+x-2=0`

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

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

`<=>x+1=0` hoặc `x-2=0`

`<=>x=-1(ktmđk)` hoặc `x=2(tmđk)`

`<=>x=2`

Vậy `S={2}.`

`3)`

`\frac{x-7}{x}=\frac{49}{x.(x-7)}+\frac{3x}{x-7}`

`(đk:x\ne0;x\ne7)`

`<=>\frac{(x-7).(x-7)}{x.(x-7)}=\frac{49}{x.(x-7)}+\frac{3x.x}{x.(x-7)}`

`=>x^{2}-7x-7x+49=49+3x^{2}`

`<=>3x^{2}+49-x^{2}+14x-49=0`

`<=>2x^{2}+14x=0`

`<=>2x.(x+7)=0`

`<=>2x=0` hoặc `x+7=0`

`<=>x=0(ktmđk)` hoặc `x=-7(tmđk)`

`<=>x=-7`

Vậy `S={-7}`

`4)`

`\frac{x+1}{x-1}-\frac{3x+1}{x^{2}-x}=1/x`

`(đk:x\ne0;x\ne1)`

`<=>\frac{x.(x+1)}{x.(x-1)}-\frac{3x+1}{x.(x-1)}=\frac{x-1}{x.(x-1)}`

`=>x^{2}+x-3x-1=x-1`

`<=>x^{2}-2x-1-x+1=0`

`<=>x^{2}-3x=0`

`<=>x.(x-3)=0`

`<=>x=0(ktmđk)` hoặc `x-3=0`

`<=>x=3`

Vậy `S={3}`

`5)`

`\frac{5+x}{3x-6}-\frac{2x-3}{2x-4}=1/2`

`(đk:x\ne2)`

`<=>\frac{x+5}{3.(x-2)}-\frac{2x-3}{2.(x-2)}=1/2`

`<=>\frac{2.(x+5)}{6.(x-2)}-\frac{3.(2x-3)}{6.(x-2)}=\frac{3.(x-2)}{6.(x-2)}`

`=>2x+10-6x+9=3x-6`

`<=>-4x+19-3x+6=0`

`<=>-7x+25=0`

`<=>-7x=-25`

`<=>x=25/7(tmđk)`

Vậy `S={25/7}.`

`6)`

`\frac{6x-x^{2}}{x^{2}-2x}+\frac{x}{x-2}=3/x`

`(đk:x\ne0;x\ne2)`

`<=>\frac{6x-x^{2}}{x.(x-2)}+\frac{x.x}{x.(x-2)}=\frac{3.(x-2)}{x.(x-2)}`

`=>6x-x^{2}+x^{2}=3x-6`

`<=>3x-6=6x`

`<=>3x-6x=6`

`<=>-3x=6`

`<=>x=-2(tmđk)`

Vậy `S={-2}.`