1. Simplifying Complex Rational Expressions
Section 7.4
Simplifying Complex Rational Expressions

2. Simplifying Rational Expressions
A complex rational expression (also called a complex fraction) has a fraction in either the numerator, or the denominator, or both. 2

3. Complex Rational Expressions
Procedure to Simplify a Complex Rational Expression: Adding and Subtracting
Add or subtract so that you have a single fraction in both the numerator and the denominator.
Divide the fraction in the numerator by the fraction in the denominator. This is done by inverting the fraction in the denominator and multiplying it by the numerator. 3

4. Example Simplify. Add the fractions in the denominator. Divide.4

5. Example
Simplify.
Add the fractions in the numerator and in the denominator.
Divide.
Simplify. 5

6. Simplifying Rational Expressions
Another way to simplify complex rational expressions is to multiply the numerator and the denominator by the LCD of all the denominators in the complex fraction.
Procedure to Simplify a Complex Rational Expression: Multiplying by the LCD
Determine the LCD of all individual denominators occurring in the numerator and denominator of the complex rational expression.
Multiply both the numerator and the denominator of the complex rational expression by the LCD.
Simplify, if possible. 6

7. Example Simplify by using the LCD.
The LCD of all the denominators is c2.
Multiply each term by c2.
Simplify. 7

8. Example Simplify by multiplying by the LCD.
The LCD of all the denominators is 8w.
Multiply each term by 8w.
Simplify. 8

9. Example
Simplify by multiplying by the LCD. 9