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NAME ______________________________________________ DATE ____________ PERIOD _____ 12-7 Rational Expressions with Unlike Denominators (Pages 678–683) The least common multiple (LCM) of two or more positive whole numbers is the least positive number that is a common multiple of all the numbers. To add or subtract rational expressions with unlike denominators, first rename the fractions so the denominators are alike, using the least common denominator of the fractions. You may need to factor one or both of the denominators first. The least common denominator (LCD) is the LCM of the denominators. Examples b. Find x 5. a. Find 5 4 2. 2y x1 3y List the prime factors of 2y and 2y 2 y 3y2 3y2 x2 LCD: (x 1)(x 2) to find the LCD. 3yy x 5 x 1 x2 Use each prime factor the greatest number of times it appears in each of the factorizations. x(x 2) (x 1)(x 2) 5(x 1) (x 1)(x 2) x 2 2x (x 1)(x 2) 5x 5 (x 1)(x 2) LCD: 2 3 y y or 6y2 Change each rational expression into an equivalent expression with the LCD. x 2 2x (5x 5) (x 1)(x 2) 5(3y) 4(2) 5 4 2 2y 3y2 2y(3y) 3y (2) 15y 15y 8 82 or 6y 6y 2 6y2 x 2 7x 5 (x 1)(x 2) Practice Find each sum or difference. Express in simplest form. 1 2 1. 2 1 2. 9 7 4. 3 2 5 5. 2 7 6. 5 3 8. 4 5x 9. 2x 10x a 7x 3x 6 a 2x x 7. x1 4x 4 x 16 xy x2 x6 7x 2 10. 2 10 5 3. 2 2 x 2x 8 x3 x 10 x4 x3 x3 x 4x 12. 2 x 3 11. 2 x4 y x 100 x 5x 6 x1 2 . 3 13. Standardized Test Practice Find 2 C 10x 7x 2 xy a 13. D 3x 6 2x 8 4x 4 x 9x 18 5x 10 7a 9 17 3 9x 8x 33 3. 4. 5. 6. 7. 8. 2 3 2 2 97 Answers: 1. 3 2. 15 x 5x 6 4x 23x 12. 2 x 9 5x 11x 12 9. 2 2 Glencoe/McGraw-Hill D 2 x 100 B 2 9x 8 x2 10x 3 10. 11. 2 2 © 2x 5 x x 20 2x 5 x4 5 x x 20 5 x4 A x5 x 16 x x 20 Glencoe Algebra 1