`6/(x-1)=9/(x+1)`

Cross multiply,

`6(x+1)=9(x-1)`

`6x+6=9x-9`

`6x-9x=-9-6`

`-3x=-15`

`x=(-15)/(-3)`

`x=5`

Check the solution:

`6/(5-1)=9/(5+1)`

`6/4=9/6`

`(3*2)/(2*2)=(3*3)/(3*2)`

`3/2=3/2`

It's true.

So, solution is x=5

`6/(x-1)=9/(x+1)`

Cross multiply,

`6(x+1)=9(x-1)`

`6x+6=9x-9`

`6x-9x=-9-6`

`-3x=-15`

`x=(-15)/(-3)`

`x=5`

Check the solution:

`6/(5-1)=9/(5+1)`

`6/4=9/6`

`(3*2)/(2*2)=(3*3)/(3*2)`

`3/2=3/2`

It's true.

So, solution is x=5