`\frac{x+1}{x-1}` `+` `\frac{x-1}{x+1}` `=` `\frac{3x+1}{(x-1)(x+1)}` `( x \ne +-1 )`

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

`x^2 +2x+1 + x^2 - 2x +1 = 3x+1`

`2x^2 +2-3x-1=0`

`2x^2 -3x+1=0`

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

`(2x^2-2x)-(x-1)=0`

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

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

`TH1:  2x-1=0`

`2x=1`

`x=1/2   (TMĐK)`

`TH2: x-1=0`

`x=1   (KTMĐK)`

Vậy phương trình có nghiệm `x= 1/2`