# Simplifying Complex Rational Expressions

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.