`a)`
`(x+2)/(x-2)-1/x=2/(x(x-2))` `(x\ne0;x\ne2)`
`<=>(x(x+2)-(x-2))/(x(x-2))=2/(x(x-2))`
`=>x(x+2)-(x-2)=2`
`<=>x^2+2x-x+2=2`
`<=>x^2+x=0`
`<=>x(x+1)=0`
`<=>` \(\left[ \begin{array}{l}x=0\\x+1=0\end{array} \right.\) `<=>` \(\left[ \begin{array}{l}x=0(KTM)\\x=-1(TM)\end{array} \right.\)
Vậy `S={-1}`
$\\$
`b)`
`(x-2)/(x+2)+3/(x-2)=(x^2-11)/(x^2-4)` `(x\ne+-2)`
`<=>((x-2)^2+3(x+2))/(x^2-4)=(x^2-11)/(x^2-4)`
`=>(x-2)^2+3(x+2)=x^2-11`
`<=>x^2-4x+4+3x+6=x^2-11`
`<=>x^2-x+10=x^2-11`
`<=>-x=-11-10`
`<=>-x=-21`
`<=>x=21` (TM)
Vậy `S={21}`
$\\$
`c)`
`(x+4)/(x+1)+x/(x-1)=(2x^2)/(x^2-1)` `(x\ne+-1)`
`<=>((x+4)(x-1)+x(x+1))/(x^2-1)=(2x^2)/(x^2-1)`
`=>(x+4)(x-1)+x(x+1)=2x^2`
`<=>x^2+3x-4+x^2+x=2x^2`
`<=>2x^2+4x-4=2x^2`
`<=>4x-4=0`
`<=>4x=4`
`<=>x=1` (KTM)
Vậy `S=∅`
