Simplifying Complex Rational Expressions
A complex rational expression, or complex fraction expression, is a rational
expression that has one or more rational expressions within its numerator or
denominator. Here are some examples:
There are two methods to simplify complex rational expressions. We will
consider them both.
Method 1
Multiplying by the LCM of all the Denominators
To simplify a complex rational expression:
a. First, find the LCM of all the denominators of all the rational
expressions occurring within both the numerator and the
denominator of the complex rational expression.
b. Then multiply by 1 using LCM LCM.
c. If possible, simplify by removing a factor of 1.
Method 2
Adding in the Numerator and the Denominator
To simplify a complex rational expression:
a. Add or subtract, as necessary, to get a single rational expression in
the numerator.
b. Add or subtract, as necessary, to get a single rational expression in
the denominator.
c. Divide the numerator by the denominator.
d. If possible, simplify by removing a factor of 1.