How does the LHS of this equation = the RHS? I know it is EASY for you, but I don't get it!.

x / (x -1) =1 / ( x - 1) + 1. Thank you for help.

Look at the right side

1 / (x - 1) + 1

Note that we can write 1 as (x - 1) / (x -1)

And we have

1 / (x -1) + (x -1) / (x - 1) so we have a common denominator

So we have

[ 1 + ( x - 1) ] / ( x - 1) =

[ 1 + x - 1 ] / ( x - 1) =

x / (x - 1) = the left side

Thank you very much. I understand it now.