You may want to review factoring polynomials first.
Common denominators of rational functions are the same as for fractions. You need to find a polynomial which both denominators go into evenly. The smaller the polynomial is, the better. For example, suppose you had to find a common denominator for 1/(x + 1) and −1/x. You would want to use x(x + 1), because x and x + 1 both go into that evenly. Of course, this multiplies out to give x2 + x. Another common denominator would be 2x2 + 2x, but that wouldn't be as good. You should always try to use the lowest common denominator (LCD, for short).