1. Adding and Subtracting Rational Expressions
Essential Questions
How do we add and subtract rational expressions?
How do we simplify complex fractions?
Holt McDougal Algebra 2
Holt Algebra 2

2. Some rational expressions are complex fractions
Some rational expressions are complex fractions. A complex fraction contains one or more fractions in its numerator, its denominator, or both. Examples of complex fractions are shown below.
Recall that the bar in a fraction represents division. Therefore, you can rewrite a complex fraction as a division problem and then simplify.

3. Example 1: Simplifying Complex Fractions
Simplify. Assume that all expressions are defined.
Write the complex fraction as division.
Multiply by the reciprocal.
Multiply.

4. Example 2: Simplifying Complex Fractions
Simplify. Assume that all expressions are defined.
Write the numerator as a single fraction.
The LCD is 2x.
Multiply by the reciprocal.

5. Example 3: Simplifying Complex Fractions
Simplify. Assume that all expressions are defined.
Write the complex fraction as division.
Multiply by the reciprocal.
Factor.

6. Example 4: Simplifying Complex Fractions
Simplify. Assume that all expressions are defined.
Write the complex fraction as division.
Multiply by the reciprocal.
Factor.

7. Example 5: Simplifying Complex Fractions
Simplify. Assume that all expressions are defined.
Write the numerator as a single fraction.
The LCD is 2x.
Multiply by the reciprocal.

8. Lesson 6.3 Practice D