Simplifying rational expressions requires good factoring skills. The twist now is that you are looking for factors that are common to both the numerator and the denominator of the rational expression.
Steps to simplify rational expressions
1) Look for factors that are common to the numerator & denominator
3) Cancel the common factor
5) After cancelling, you are left with 1/(x-1)
6) The final simplified rational expression is valid for all values of x except 0 and 1.