**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.