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Mastering Addition and Subtraction of Rational Expressions

This lesson focuses on enabling students to find the Lowest Common Denominator (LCD) and perform addition and subtraction of rational expressions with both like and unlike denominators. Key concepts include the necessity of a common denominator for fraction operations and ensuring that addition and subtraction occur only in the numerator. Students will learn through examples involving monomials and binomials, emphasizing the importance of simplification, factoring, and distributing negatives in their calculations.

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Mastering Addition and Subtraction of Rational Expressions

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  1. Adding & Subtracting Rational Expressions Objectives Students will be able to find the Lowest common denominator Students will be able to add & subtract Rational Expressions with like and unlike denominators.

  2. We know that… • …in order to add or subtract any fraction, there must be a common denominator. • …adding and subtracting only happen in the numerator (top) of the fraction, NEVER IN THE DENOMINATOR (BOTTOM). • …we can take this same approach with RATIONAL EXPRESSIONS (ALGEBRAIC FRACTIONS).

  3. For Instance

  4. Example: Monomials in Denominator & Numerator Always, always Simplify! a) b) Add Numerators Common Denominators Always, always Simplify! Add Numerators Common Denominators

  5. Example: Binomials in Denominator a) b) c) d)

  6. Example: Binomials in Numerator & Denominator a) b) Distribute the Negative!! Always Look to Factor

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