In this Section:
In this section, we review how to simplify complex fractions. More specifically, we refer to these complex fractions as complex rational expressions. These complex rational expressions contain rational expressions in the numerator, denominator, or both numerator and denominator. There are two basic methods that are employed to simplify complex rational expressions. The first method calls for us to simplify the numerator and denominator of the complex rational expression separately. Once we are done simplifying, we perform the main division and simplify once more. The second method relies on finding the LCD or least common denominator for all of the smaller denominators in the problem. Once we have obtained the LCD, we multiply the numerator and denominator of the complex fraction by the LCD and simplify. In most cases, the LCD method is faster and preferred. Either method produces the same result after we simplify.