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LESSON 5.6 Answers for the lesson “Solve Rational Equations” Skill Practice 26. The student “cross multiplied” 1. cross multiplying 2. 4; 4 is not in the domain of the equation because you cannot divide by zero. 3. Graph both sides of the equation. Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. If the graphs intersect at a possible solution, then it is a solution. If the graphs do not intersect at a possible solution, then it is an extraneous solution. the fractions on the left side of the equation. Both sides of the equation should have been multiplied by the LCD, 2x 2; 1 2x 2 4 3 2x 2 } 1 }2 5 2x 2(1), x 3x 1 8 5 2x 2. 27. The student simply added 4. 4 5. 6 6. 5 numerators and denominators on the left side of the equation. Both sides of the equation should have been multiplied by the LCD, 6x; 7. 2 8. 3 9. 21 6x1 }x 1 } 5 6x 1 } , 62 x2 10. 61 11. no solution 12. 6 13. A 23 45 30 1 23x 5 270. 14. 1, 4 } 23 6 Ï 129 4 15. 4 16. } 7 17. 2} 3 18. 1, 6 } 21 6 Ï 79 19. } 3 20. 22, 3 21. 1 3 22. 2}, 2 2 5 23. 2}, 8 2 24. no solution 25. 0, 7 5 28. C 2x 6 29. Sample answer: } 5 }; x21 x15 5 12 4 }1}5} 3 x x 30. Always true; when x 5 a, the denominators of the fractions are zero. 31. Sometimes true; the equation will have exactly one solution except when a 5 3. 32. Always true; the only apparent solution is an extraneous solution. Algebra 2 Answer Transparencies for Checking Homework 177 Problem Solving 38. a. 33. 26 serves f (x) 5 }}} 3 2 8 9 34. a. } 5 } x 4.38 1 x b. Skater 1: 39.42 km/h, 20.27x 3 1 1.4x 2 1 1.05x 1 39.4 28.25x 1 53.1x 2 7.82x 1 138 b. about $.29 per min c. 2002 Skater 2: 35.04 km/h c. About 0.23 h. Sample answer: Divide the distance, 9 kilometers, by the rate, 39.42 kilometers per hour, to find the time. 35. 1995 5 5 36. a. } room, }t room 8 Copyright © Houghton Mifflin Harcourt Publishing Company. All rights reserved. 5t 1 40 b. }; the expression 8t represents the amount of work done by you and your friend while working together for 5 hours. 3 5 1 c. }t 5 } l t 5 13} h; when 8 3 working together, you and your friend can complete one room. } 1 1 Ï5 37. } 2 Algebra 2 Answer Transparencies for Checking Homework 178