`(x+1)/(x-1)= 2/(2x-1) + 2/(x-1)`

Subtract `2/(x-1)` from both sides

`==gt (x+1)/(x-1) - 2/(x-1) = 2/(2x-1)`

Cobine numerators:

`==gt (x+1-2)/(x-1) = 2/(2x-1) `

`==gt (x-1)/(x-1) = 2/(2x-1)`

Simplify left side:

`==gt 1 = 2/(2x-1)`

==> 2x-1 = 2

==> 2x = 3

**==> x= 3/2**