Adding and Subtracting Rational Expressions

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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

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.

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

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.

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

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

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.

Lesson 6.3 Practice D