Solution the expression on the right side of the

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Unformatted text preview: are equivalent. 4x 2 9 x2 9 4 4y 2 y2 1 4 Solution To write the expression on the left side of the equation in the form given on the right side, multiply the numerators and denominators of both terms by 1. 4 4x2 9 1 4x2 4 91 4 4y2 1 4 1 4 4y2 x2 9 4 y2 1 4 Now try Exercise 29. Rewriting with Negative Exponents Example 5 Rewrite each expression using negative exponents. a. 1 4x 2x 2 b. 2 2 5x 3 1 3 5 4x x 2 Solution 4x 4x 1 2x 2 2 1 2x 2 2 b. Begin by writing the second term in exponential form. a. 2 5x 3 1 x 3 5 4x 2 2 5x 3 2 x 5 1 x1 2 3 x 3 5 4x 2 3 4x 5 12 2 Now try Exercise 39. Example 6 Writing a Fraction as a Sum of Terms Rewrite each fraction as the sum of three terms. a. x2 4x 2x 8 b. x 2x2 x 1 Solution a. x2 4x 2x 8 x2 4x 8 2x 2x 2x 4 x 2 2 x Now try Exercise 43. b. x 2x2 x 1 x 12 x x1 2 2x2 x1 2 2x 3 2 1 12 x x 12 333202_0A07.qxd 12/8/05 11:27 AM Page A75 Appendix A.7 A.7 A75 Errors and the Algebra of Calculus Exercises VOCABULARY CHECK: Fill in the blanks. 1. To write the expression 2 with negative exponents, move x change the sign of the exponent. x to the ________ and 2. When dividing fractions, multiply by the ________. 31. 1. 2x 3y 4 2x 3y 3x 2 5z 3x 2 x2 49 4 2. 5z x2 1 12 32. In Exercises 1–18, describe and correct the error. 3. 4 2x 16x 5. 5z 6z 11. 13. x 3 2x 1 1 15. x 2 3 17. x 4 y 2 1 1 a 2 51 2 y y 1 xy 14. b xx x x 1 1 1 18. 2y y 5 x y y x 38. 1 2 2x 2 x 2 1 2y In Exercises 19–38, insert the required factor in the parentheses. 3x 2 5 2 21. 3x 2 1 3x 23. x2 x3 26. x2 2x 30. 2x 9y2 16 4x x2 1 3x 7 32 x2 1 2x 32 6x 5 2 x2 1 169 2x 3 45. 2x 2 47. 3x3 5 x 3 3 1 x1 4x 3 1 2 x1 3x 2 10x 5 52 1 3 t 7 3 4x 1 5x 3 2x 2 43 3x 1 x1 8y2 1 2x 6 3 t 4 73 2 13 1 3x 1 2x 1 15 3 1 2 2x 32 1 1 43 3t 14 28 32 3 3x2 4 3x 40. 13 2x 7x 2x 4 x4 42. 3 x x6 1 x 12 x x 8 3 9x 3 1 x2 2 16 x2 5x x 4x 3 7x 2 44. 1 46. 13 x 5x 2 x 3 x4 48. x3 5x 2 x2 2x 5 x3 4 3x 3 x3 5x 2 5x 4 3x 2 In Exercises 49 – 60, simplify the expression. 3 y 5 2 49. y2 50. x2 9x2 In Exercises 43– 48, write the fraction as a...
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