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Adding and Subtracting Rational Expressions

Learn how to simplify complex fractions by rewriting them as divisions, multiplying by the reciprocal, and factoring. Explore examples, techniques, and step-by-step instructions to enhance your understanding of adding and subtracting rational expressions. Practice Lesson 6.3.D from Holt McDougal Algebra 2.

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Adding and Subtracting Rational Expressions

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  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. 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

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