`color{#ffccf5}{#}color{#ffbaf1}{d}color{#ffa1ec}{t}color{#ff8ae8}{t}`

`x^2+(x^2)/((x-1)^2)=8\ (x\ne1)`

Đặt `t=x-1`

`-> x=t+1`

Pt trở thành:

`(t+1)^2+((t+1)^2)/(t^2)=8`

`t^2+2t+1+(t^2+2t+1)/(t^2)=8`

`t^2+2t+1+1+2/t+1/(t^2)=8`

`t^2+1/(t^2)+2(t+1/t)=6`

Đặt: `v=t+1/t`
`-> v^2=t^2+1/(t^2)+2`

`-> t^2+1/(t^2)=v^2-2`

Pt trở thành:

`v^2-2+2v=6`

`v^2-2v+4v-8=0`

`v(v-2)+4(v-2)=0`

`(v+4)(v-2)=0`

`v=-4` hoặc `v=-2`

`+) v=-4->t+1/t=-4`

`-> t=-2+-\sqrt(3)`

`-> x-1=-2+-\sqrt(3)`

`-> x=-1+-\sqrt(3)\ (tm)`

`+) v=2->t+1/t=2`

`-> t=1`

`-> x-1=1`

`-> x=2\ (tm)`

Vậy `S={2;-1+-\sqrt(3)}`