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Name_____________________________________ Class____________________________ Date________________ Lesson 12-6 Solving Rational Equations Lesson Objectives 1 Solve rational equations 2 Solve proportions NAEP 2005 Strand: Algebra Topics: Algebraic Representations; Equations and Inequalities Local Standards: ____________________________________ Vocabulary. All rights reserved. A rational equation is Example. 1 Solving by Factoring Solve x62 5 5x 2 1. Check the solution. ( x6 ) (5x 1) ( x6 ) (5x) 2 6 x2 x 6 2 5 1 ✓ Property. Collect terms on one side. 0 or x . Simplify. )0 Check Use the (1) 0 )( ( Multiply each side by the LCD, 0 x or 6 2 Factor the expression. Use the Property. Solve. 5 1 ✓ Quick Check. 1. Solve each equation. Check your solution. 1 51 a. 13 1 3x 6 224 Algebra 1 Lesson 12-6 5 b. m 5 22 1 2 m Daily Notetaking Guide © Pearson Education, Inc., publishing as Pearson Prentice Hall. 2 Name_____________________________________ Class____________________________ Date ________________ Example. 2 Work-Rate Problem Renee can mow the lawn in 20 minutes. Joanne can do the same job in 30 minutes. How long will it take them if they work together? Define Let n the time to complete the job if they work together (in minutes). All rights reserved. Person Relate Write Work Rate (part of job/min.) Renee n Joanne n Part of job done Renee’s part done Joanne’s part done complete job n n 1 ( n n ) 3n 2n © Pearson Education, Inc., publishing as Pearson Prentice Hall. Time Worked (min.) It will take them (1) Multiply each side by the LCD, Use the Simplify. Simplify. . Property. minutes to mow the lawn together. Quick Check. 2. Peggy can pick a bushel of apples in 45 min. Peter can pick a bushel of apples in 75 min. How long will it take them to pick a bushel if they work together? Daily Notetaking Guide Algebra 1 Lesson 12-6 225 Name_____________________________________ Class____________________________ Date ________________ Example. 3 4 3 Checking to Find an Extraneous Solution Solve xx 1 2 1 5 x 2 1. (x 3)( ) x (x 1) Write cross products. 3 4x Use the Property. 2 4x Combine terms. 2 Subtract from each side. x (x )(x )0 3 Check 1 Factor. 0 Use the Zero-Product Property. Simplify. All rights reserved. x 4 1 The equation has no solution because Undefined! There is no division by . makes the denominator equal . © Pearson Education, Inc., publishing as Pearson Prentice Hall. Quick Check. 3. Solve each equation. Check your solution. 5 a. a3 5 a 2 2 4 b. n5 5 n 1 1 c. 22 5 2 1 d. w w2 1 5 w 2 1 c 226 2 c 11 2 Algebra 1 Lesson 12-6 Daily Notetaking Guide