Mini-Lecture 7.3: Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator | Montgomery College - Edubirdie

University:
Montgomery College
Course:
MATH 130: Elements of Mathematics I: Mathematical Reasoning and Number Systems
Academic year:

2023
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379

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1
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blakestar2o1o

Mini-Lecture 7.3 Adding and Subtracting Rational Expressions with Common Denominators and Least Common Denominator Learning Objectives: 1. 2. 3. 4. Add and subtract rational expressions with the same denominator. Find the least common denominator of a list of rational expressions. Write a rational expression as an equivalent expression whose denominator is given. Key Vocabulary: least common denominator (LCD), equivalent expressions. Examples: 1. Add or subtract as indicated. Simplify the result if possible. a) d) 3 4 + 12x 12x b) m 2 − 7m 12 + m−3 m−3 e) 8a + 2b 8a − 2b − 2 2 3x + 2 x + 4x − 21 2 − c) 7y 2 −7y + y −1 y −1 c) 4 6 , 2 3a + 27 a + 9a 2x − 5 x + 4x − 21 2 2. Find the LCD for each list of rational expressions. a) 1 20x 5 , 1 36x 4 b) 2 3 , x +3 x −5 3. Rewrite each rational expression as an equivalent rational expression with the given denominator. a) 3 ? = 8m 72m b) c) a ? = 2 a + 3b a − 9b 2 d) x ? = x + 4 5x + 20 −25 x + 2x − 3x 3 2 = ? x(x − 1)(x + 3)(x + 5) Teaching Notes: • • • Most students need a review of finding the LCD for numerical fractions. Many students have a difficult time finding the LCD. Refer them back to the process they use when finding the LCD for numerical fractions. Each section in the text has 3 worksheets in the Extra Practice featuring differentiated learning. Answers: 1a) 7 1 ; 1b) 2b; 1c) 7y; 1d) m-4; 1e) ; 2a) 180x5; 2b) x2 – 2x –15; 2c) 3a2 + 27a; 12x x−3 3a) 27; 3b) 5x; 3c) a2 – 3ab; 3d) -25x – 125

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