Rational Expressions What you’ll learn To simplify rational expressions. To multiply and divide rational expressions. Vocabulary Rational expression Simplest form

Take a note: A rational expression is the quotient of two polynomials. It is helpful to think of rational expressions as ratios, as fractions, or as quotients. A rational expression is in the simplest form when the numerator and denominator are polynomials that have no common divisors. Examples: In simplest form Not in simplest form

Problem 1: Simplifying a Rational Expression

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Problem 2: Multiplying Rational Expression. Factor all polynomials Simplify Answer

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Problem 3: Dividing Rational Expressions Multiply by the reciprocal Factor and get -1 from (2-x) Simplify

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Problem 4: Using Expression to solve a Problem. Your community is building a park. It wants to fence in a play space for toddlers. It wants the maximum area for a given amount of fencing. Which shape, a square or a circle, provides a more efficient use of fencing? 0ne measure of efficiency is the ratio of the area fenced to fencing used, or area to perimeter, Which of the two shapes has the greatest ratio? Square Circle Define area and perimeter

Express s and r in terms of a common variable. Write the ratios. Substitute for s and r Simplify

Classwork odd Homework even TB pgs. 530-531 exercises 8-44