Mini-Lecture 7.5: Solving Equations Containing Rational Expressions | 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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244

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1
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Seena4tm5

Mini-Lecture 7.5 Solving Equations Containing Rational Expressions Learning Objectives: 1. Solve equations containing rational expressions. 2. Solve equations containing rational expressions for a specified variable. 3. Key Vocabulary: rational expressions. Examples: 1. Solve each equation and check each solution. a) x x − =8 3 9 b) 4x −8 = x 5 c) x −3 x +4 = 7 3 d) x + 10 9 = x −5 5−x e) 4 4 + =6 x − 4 2x − 8 f) x 7 +6= x −7 x−7 g) −5x 2x 6x − 4 = + 3x + 3 6x + 6 x + 1 h) i) −2 3 15 − = 2 m + 5 m − 5 m − 25 j) 1 1 x−7 + = x x −8 x −8 x+4 x + 2x − 15 2 − 4 x + 10x + 25 2 = x−4 x + 2x − 15 2 2. Solve each equation for the indicated variable. a) 1 1 + = c for b a b b) A = 1 h ( B + b ) for B 2 c) F= −GMm r2 for m Teaching Notes: • • • • Remind students to always determine the values for x that will make the denominators of the equation equal to zero. Some students prefer to create equivalent expressions using the LCD then set numerators equal. Most students have difficulty solving a formula for a specific variable. To help students focus on solving a formula for a specific variable, encourage them to write the variable with a different color pencil. Answers: 1a) 36; 1b) -40; 1c) -37/4; 1d) -19; 1e) 5; 1f) no solution; 1g) ½; 1h) 1; 1i) -4; 1j) -13; 2a) b = 2A 2 A − bh Fr 2 a − b or ; 2b) B = ; 2c) m = − GM h h ac − 1

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