Explanation Procedure used: Decomposing a rational expression into partial fractions: Consider a rational expression of the form P ( x ) Q ( x ) , such that P ( x ) and Q ( x ) have no common factor other than 1 or –1. 1 If the degree of P ( x ) is greater than or equal to the degree of Q ( x ) , divide to express P ( x ) Q ( x ) as a quotient + remainder divided by divisor and follow steps (2)-(5) to decompose the resulting rational expression. 2 If the degree of P ( x ) is less than the degree of Q ( x ) , factor Q ( x ) into linear factors of the form ( p x + q ) n and/or quadratic factors of the form ( a x 2 + b x + c ) m . Any quadratic factor a x 2 + b x + c must be irreducible, which means that it cannot be factored into linear factors with rational coefficients. 3 Assign to each linear factor ( p x + q ) n the sum of n partial fractions: A 1 p x + q + A 2 ( p x + q ) 2 + ⋯ + A n ( p x + q ) n 4 Assign to each quadratic factor ( a x 2 + b x + c ) m the sum of m partial fractions: B 1 x + C 1 ( a x 2 + b x + c ) + B 2 x + C 2 ( a x 2 + b x + c ) 2 + ⋯ + B m x + C m ( a x 2 + b x + c ) m 5 Apply algebraic methods, to find the constants in the numerators of the partial fractions. Calculation: Consider the given rational expression 3 x 2 − 11 x − 26 ( x 2 − 4 ) ( x + 1 ) . Factorize the denominator as mentioned below. 3 x 2 − 11 x − 26 ( x 2 − 4 ) ( x + 1 ) = 3 x 2 − 11 x − 26 ( x + 2 ) ( x − 2 ) ( x + 1 ) Here, the degree of the numerator is less than the denominator. Since there are no quadratic factors in the expression, assign three constants A, B and C to each linear factor such that, 3 x 2 − 11 x − 26 ( x + 2 ) ( x − 2 ) ( x + 1 ) = A x + 2 + B x − 2 + C x + 1 . In order to determine the constants, add the rational terms on the right side of the equation. 3 x 2 − 11 x − 26 ( x + 2 ) ( x − 2 ) ( x + 1 ) = A ( x − 2 ) ( x + 1 ) + B ( x + 2 ) ( x + 1 ) + C ( x + 2 ) ( x − 2 ) ( x + 2 ) ( x − 2 ) ( x + 1 ) Further, equate the numerators. 3 x 2 − 11 x − 26 = A ( x − 2 ) ( x + 1 ) + B ( x + 2 ) ( x + 1 ) + C ( x + 2 ) ( x − 2 ) Since, the above equation containing the constants A, B and C is true for all x , Therefore, for every x the equation is valid. To eliminate A and B substitute x = − 1 then x + 1 = 0 . Therefore, 3 ( − 1 ) 2 − 11 ( − 1 ) − 26 = A ( − 1 − 2 ) ( − 1 + 1 ) + B ( − 1 + 2 ) ( − 1 + 1 ) + C ( − 1 + 2 ) ( − 1 − 2 ) 3 + 11 − 26 = A ( − 3 ) ( 0 ) + B ( 1 ) ( 0 ) + C ( 1 ) ( − 3 ) − 12 = − 3 C C = 4 To eliminate A and C , substitute x = 2 then x − 2 = 0 . Therefore, 3 ( 2 ) 2 − 11 ( 2 ) − 26 = A ( 2 − 2 ) ( 2 + 1 ) + B ( 2 + 2 ) ( 2 + 1 ) + C ( 2 + 2 ) ( 2 − 2 ) 3 ( 4 ) − 22 − 26 = A ( 0 ) ( 3 ) + B ( 4 ) ( 3 ) + C ( 4 ) ( 0 ) − 36 = 12 B B = − 3 To eliminate B and C

6th Edition

ISBN: 2810000027802

Author: BITTINGER

Publisher: PEARSON

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Chapter 6.8, Problem 5E

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To decompose: The expression 3x2−11x−26(x2−4)(x+1) into partial fractions and check the answer using a graphing calculator.

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Chapter 6.8, Problem 4E

Chapter 6.8, Problem 6E

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Chapter 6 Solutions

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Ch. 6.1 - In Exercises 16, match the system of equations...Ch. 6.1 - In Exercises 16, match the system of equations...Ch. 6.1 - Prob. 3E Ch. 6.1 - Prob. 4E Ch. 6.1 - Prob. 5E Ch. 6.1 - Prob. 6E Ch. 6.1 - Prob. 7E Ch. 6.1 - Prob. 8E Ch. 6.1 - Prob. 9E Ch. 6.1 - Prob. 10E

Ch. 6.1 - Prob. 11E Ch. 6.1 - Prob. 12E Ch. 6.1 - Solve graphically. x y = 6, y = 2x Ch. 6.1 - Prob. 14E Ch. 6.1 - Prob. 15E Ch. 6.1 - Prob. 16E Ch. 6.1 - Prob. 17E Ch. 6.1 - Prob. 18E Ch. 6.1 - Prob. 19E Ch. 6.1 - Prob. 20E Ch. 6.1 - Prob. 21E Ch. 6.1 - Prob. 22E Ch. 6.1 - Prob. 23E Ch. 6.1 - Prob. 24E Ch. 6.1 - Prob. 25E Ch. 6.1 - Prob. 26E Ch. 6.1 - Prob. 27E Ch. 6.1 - Prob. 28E Ch. 6.1 - Prob. 29E Ch. 6.1 - Prob. 30E Ch. 6.1 - Solve using the elimination method. Also determine...Ch. 6.1 - Prob. 32E Ch. 6.1 - Prob. 33E Ch. 6.1 - Solve using the elimination method. Also determine...Ch. 6.1 - Solve using the elimination method. 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Aarons boat travels 45 mi downstream in 3...Ch. 6.1 - Prob. 69E Ch. 6.1 - Prob. 70E Ch. 6.1 - Prob. 71E Ch. 6.1 - Prob. 72E Ch. 6.1 - Prob. 73E Ch. 6.1 - Prob. 74E Ch. 6.1 - Prob. 75E Ch. 6.1 - Prob. 76E Ch. 6.1 - Prob. 77E Ch. 6.1 - Prob. 78E Ch. 6.1 - Prob. 79E Ch. 6.1 - Prob. 80E Ch. 6.1 - Prob. 81E Ch. 6.1 - Prob. 82E Ch. 6.1 - Prob. 83E Ch. 6.1 - Prob. 84E Ch. 6.1 - Prob. 85E Ch. 6.1 - Antifreeze Mixtures. An automobile radiator...Ch. 6.1 - Prob. 87E Ch. 6.1 - Prob. 88E Ch. 6.1 - Prob. 89E Ch. 6.2 - Prob. 1E Ch. 6.2 - Prob. 2E Ch. 6.2 - Prob. 3E Ch. 6.2 - Prob. 4E Ch. 6.2 - Prob. 5E Ch. 6.2 - Prob. 6E Ch. 6.2 - Prob. 7E Ch. 6.2 - Prob. 8E Ch. 6.2 - Prob. 9E Ch. 6.2 - Prob. 10E Ch. 6.2 - Prob. 11E Ch. 6.2 - Prob. 12E Ch. 6.2 - Solve the system of equations. 2x+z=1,3y2z=6,x2y=9 Ch. 6.2 - Prob. 14E Ch. 6.2 - Solve the system of equations....Ch. 6.2 - Solve the system of equations....Ch. 6.2 - Paralympic Medals. At the 2014 Paralympic Games in...Ch. 6.2 - Restaurant Meals. 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Use the following facts...Ch. 6.2 - Prob. 49E Ch. 6.2 - Prob. 50E Ch. 6.2 - Prob. 51E Ch. 6.2 - Prob. 52E Ch. 6.3 - Determine the order of the matrix. [163205]Ch. 6.3 - Prob. 2E Ch. 6.3 - Determine the order of the matrix. [2 4 0 9]Ch. 6.3 - Prob. 4E Ch. 6.3 - Prob. 5E Ch. 6.3 - Prob. 6E Ch. 6.3 - Prob. 7E Ch. 6.3 - Prob. 8E Ch. 6.3 - Prob. 9E Ch. 6.3 - Prob. 10E Ch. 6.3 - Prob. 11E Ch. 6.3 - Prob. 12E Ch. 6.3 - Prob. 13E Ch. 6.3 - Prob. 14E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 17E Ch. 6.3 - Prob. 18E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 24E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 26E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 28E Ch. 6.3 - Prob. 29E Ch. 6.3 - Prob. 30E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 32E Ch. 6.3 - Prob. 33E Ch. 6.3 - Prob. 34E Ch. 6.3 - Prob. 35E Ch. 6.3 - Prob. 36E Ch. 6.3 - Prob. 37E Ch. 6.3 - Prob. 38E Ch. 6.3 - Solve the system of equations using Gaussian...Ch. 6.3 - Prob. 40E Ch. 6.3 - Use Gaussian elimination or GaussJordan...Ch. 6.3 - Prob. 42E Ch. 6.3 - Prob. 43E Ch. 6.3 - Prob. 44E Ch. 6.3 - Prob. 45E Ch. 6.3 - Prob. 46E Ch. 6.3 - Prob. 47E Ch. 6.3 - Prob. 48E Ch. 6.3 - Prob. 49E Ch. 6.3 - Prob. 50E Ch. 6.3 - Prob. 51E Ch. 6.3 - Prob. 52E Ch. 6.3 - In Exercises 53 and 54, three solutions of the...Ch. 6.3 - Prob. 54E Ch. 6.3 - Prob. 55E Ch. 6.3 - Prob. 56E Ch. 6.3 - Prob. 57E Ch. 6.3 - Prob. 58E Ch. 6.3 - Prob. 59E Ch. 6.3 - Prob. 60E Ch. 6.3 - Prob. 61E Ch. 6.3 - Prob. 62E Ch. 6.4 - Prob. 1E Ch. 6.4 - Prob. 2E Ch. 6.4 - Prob. 3E Ch. 6.4 - Prob. 4E Ch. 6.4 - For Exercises 520, let...Ch. 6.4 - Prob. 6E Ch. 6.4 - Prob. 7E Ch. 6.4 - Prob. 8E Ch. 6.4 - Prob. 9E Ch. 6.4 - Prob. 10E Ch. 6.4 - Prob. 11E Ch. 6.4 - Prob. 12E Ch. 6.4 - Prob. 13E Ch. 6.4 - For Exercises 520, let...Ch. 6.4 - For Exercises 520, let...Ch. 6.4 - Prob. 16E Ch. 6.4 - Prob. 17E Ch. 6.4 - Prob. 18E Ch. 6.4 - Prob. 19E Ch. 6.4 - Prob. 20E Ch. 6.4 - Prob. 21E Ch. 6.4 - Prob. 22E Ch. 6.4 - Prob. 23E Ch. 6.4 - Prob. 24E Ch. 6.4 - Prob. 25E Ch. 6.4 - Prob. 26E Ch. 6.4 - Prob. 27E Ch. 6.4 - Prob. 28E Ch. 6.4 - Produce. 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Then find the...Ch. 6.7 - Graph the system of inequalities. Then find the...Ch. 6.7 - Prob. 58E Ch. 6.7 - Prob. 59E Ch. 6.7 - Graph the system of inequalities. Then find the...Ch. 6.7 - Find the maximum value and the minimum value of...Ch. 6.7 - Find the maximum value and the minimum value of...Ch. 6.7 - Prob. 63E Ch. 6.7 - Prob. 64E Ch. 6.7 - Prob. 65E Ch. 6.7 - Maximizing Income. Golden Harvest Foods makes...Ch. 6.7 - Prob. 67E Ch. 6.7 - Prob. 68E Ch. 6.7 - Prob. 69E Ch. 6.7 - Prob. 70E Ch. 6.7 - Prob. 71E Ch. 6.7 - Prob. 72E Ch. 6.7 - Minimizing Transportation Cost. An airline with...Ch. 6.7 - Minimizing Transportation Cost. Suppose that in...Ch. 6.7 - Maximizing Profit. It takes Fena Tailoring 3 hr of...Ch. 6.7 - Maximizing Profit. Cambridge Metal Works...Ch. 6.7 - Minimizing Nutrition Cost. Suppose that it takes...Ch. 6.7 - Prob. 78E Ch. 6.7 - Prob. 79E Ch. 6.7 - Prob. 80E Ch. 6.7 - Prob. 81E Ch. 6.7 - Prob. 82E Ch. 6.7 - Prob. 83E Ch. 6.7 - Prob. 84E Ch. 6.7 - Prob. 85E Ch. 6.7 - Graph the system of inequalities. y x + 1, y x2 Ch. 6.7 - Prob. 87E Ch. 6.7 - Prob. 88E Ch. 6.7 - Prob. 89E Ch. 6.7 - Prob. 90E Ch. 6.7 - Prob. 91E Ch. 6.8 - Prob. 1E Ch. 6.8 - Prob. 2E Ch. 6.8 - Prob. 3E Ch. 6.8 - Prob. 4E Ch. 6.8 - Prob. 5E Ch. 6.8 - Prob. 6E Ch. 6.8 - Prob. 7E Ch. 6.8 - Prob. 8E Ch. 6.8 - Prob. 9E Ch. 6.8 - Prob. 10E Ch. 6.8 - Prob. 11E Ch. 6.8 - Prob. 12E Ch. 6.8 - Prob. 13E Ch. 6.8 - Decompose into partial fractions. Check your...Ch. 6.8 - Decompose into partial fractions. Check your...Ch. 6.8 - Prob. 16E Ch. 6.8 - Prob. 17E Ch. 6.8 - Prob. 18E Ch. 6.8 - Prob. 19E Ch. 6.8 - Decompose into partial fractions. Check your...Ch. 6.8 - Prob. 21E Ch. 6.8 - Prob. 22E Ch. 6.8 - Prob. 23E Ch. 6.8 - Prob. 24E Ch. 6.8 - Decompose into partial fractions. Check your...Ch. 6.8 - Prob. 26E Ch. 6.8 - Prob. 27E Ch. 6.8 - Prob. 28E Ch. 6.8 - Prob. 29E Ch. 6.8 - Prob. 30E Ch. 6.8 - Prob. 31E Ch. 6.8 - Prob. 32E Ch. 6.8 - Prob. 33E Ch. 6.8 - Prob. 34E Ch. 6.8 - Prob. 35E Ch. 6 - Determine whether the statement is true or false....Ch. 6 - Prob. 2MC Ch. 6 - Prob. 3MC Ch. 6 - Prob. 4MC Ch. 6 - Prob. 5MC Ch. 6 - Prob. 6MC Ch. 6 - Prob. 7MC Ch. 6 - Prob. 8MC Ch. 6 - Prob. 9MC Ch. 6 - Prob. 10MC Ch. 6 - Prob. 11MC Ch. 6 - Prob. 12MC Ch. 6 - Prob. 13MC Ch. 6 - Prob. 14MC Ch. 6 - Prob. 15MC Ch. 6 - Prob. 16MC Ch. 6 - Prob. 17MC Ch. 6 - Prob. 18MC Ch. 6 - Prob. 19MC Ch. 6 - Prob. 20MC Ch. 6 - Prob. 21MC Ch. 6 - Prob. 1RE Ch. 6 - Prob. 2RE Ch. 6 - Prob. 3RE Ch. 6 - Prob. 4RE Ch. 6 - Prob. 5RE Ch. 6 - Prob. 6RE Ch. 6 - Prob. 7RE Ch. 6 - Prob. 8RE Ch. 6 - Prob. 9RE Ch. 6 - Prob. 10RE Ch. 6 - Prob. 11RE Ch. 6 - Prob. 12RE Ch. 6 - Prob. 13RE Ch. 6 - Prob. 14RE Ch. 6 - Prob. 15RE Ch. 6 - Prob. 16RE Ch. 6 - Prob. 17RE Ch. 6 - Prob. 18RE Ch. 6 - Prob. 19RE Ch. 6 - Prob. 20RE Ch. 6 - Prob. 21RE Ch. 6 - Prob. 22RE Ch. 6 - Prob. 23RE Ch. 6 - Solve the system of equations using Gaussian...Ch. 6 - Prob. 25RE Ch. 6 - Coins. 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Jackson is taking a test...Ch. 6 - Decompose into partial fractions. 5(x+2)2(x+1)Ch. 6 - Prob. 61RE Ch. 6 - Prob. 62RE Ch. 6 - Prob. 63RE Ch. 6 - Prob. 64RE Ch. 6 - Prob. 65RE Ch. 6 - Prob. 66RE Ch. 6 - Prob. 67RE Ch. 6 - Prob. 68RE Ch. 6 - Prob. 69RE Ch. 6 - Prob. 1T Ch. 6 - Prob. 2T Ch. 6 - Prob. 3T Ch. 6 - Prob. 4T Ch. 6 - Prob. 5T Ch. 6 - Prob. 6T Ch. 6 - Prob. 7T Ch. 6 - Prob. 8T Ch. 6 - Prob. 9T Ch. 6 - Prob. 10T Ch. 6 - Prob. 11T Ch. 6 - Prob. 12T Ch. 6 - Prob. 13T Ch. 6 - Prob. 14T Ch. 6 - Prob. 15T Ch. 6 - Prob. 16T Ch. 6 - Prob. 17T Ch. 6 - Prob. 18T Ch. 6 - Prob. 19T Ch. 6 - Prob. 20T Ch. 6 - Prob. 21T Ch. 6 - Prob. 22T Ch. 6 - Prob. 23T Ch. 6 - Prob. 24T Ch. 6 - Prob. 25T

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To decompose: The expression 3 x 2 − 11 x − 26 ( x 2 − 4 ) ( x + 1 ) into partial fractions and check the answer using a graphing calculator.

Solution Summary: The author explains how to decompose a rational expression into partial tions.

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To decompose: The expression 3x2−11x−26(x2−4)(x+1) into partial fractions and check the answer using a graphing calculator.

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Chapter 6 Solutions