So you need a common denominator. Since the two denominators have no common factors, the common denominator is simply the product of the two denominators, hence:
Here is a quick shortcut anytime you have the sum or difference of 1 over something plus/minus 1 over something else:
In other words, the sum/difference of the denominators over the product of the denominators.
By the way, next time use parentheses so that there is no confusion about what you mean when you render your problem. This one, if I interpreted it correctly, should have been written (1/x) - (1/(x - 1)) to differentiate it from (1/x) - (1/x) - 1.
