Explanation Given: The function is 3 x 2 + 12 x − 20 x 4 − 8 x 2 + 16 Approach: Let Q ( x ) can be factorized as Q ( x ) = ( a 1 x + b 1 ) ( a 2 x + b 2 ) ... ( a n x + b n ) Partial fraction decomposition is given by P ( x ) Q ( x ) = A 1 a 1 x + b 1 + A 2 a 2 x + b 2 + ... + A n a n x + b n Calculation: Partial decomposition of the given function is given by 3 x 2 + 12 x − 20 x 4 − 8 x 2 + 16 = 3 x 2 + 12 x − 20 ( x − 2 ) 2 ( x + 2 ) 2 = A ( x − 2 ) + B ( x − 2 ) 2 + C ( x + 2 ) + D ( x + 2 ) 2 = A ( x 3 + 2 x 2 − 4 x − 8 ) + B ( x 2 + 4 x + 4 ) + C ( x 3 − 2 x 2 − 4 x + 8 ) + D ( x 2 − 4 x + 4 ) ( x − 2 ) 2 ( x + 2 ) 2 = x 3 ( A + C ) + x 2 ( 2 A + B − 2 C + D ) + x ( − 4 A + 4 B − 4 C − 4 D ) − 8 A + 4 B + 8 C + 4 D ( x − 2 ) 2 ( x + 2 ) 2 Multiply each side by the common denominator ( x − 2 ) 2 ( x + 2 ) 2 3 x 2 + 12 x − 20 = x 3 ( A + C ) + x 2 ( 2 A + B − 2 C + D ) + x ( − 4 A + 4 B − 4 C − 4 D ) − 8 A + 4 B + 8 C + 4 D Compare both the sides A + C = 0 … ( 1 ) 2 A + B − 2 C + D = 3 … ( 2 ) − 4 A + 4 B − 4 C − 4 D = 12 … ( 3 ) − 8 A + 4 B + 8 C + 4 D = − 20 … ( 4 ) By equation ( 1 ) C = − A Substitute − A for C in equations ( 2 ) , ( 3 ) and ( 4 )

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ISBN: 2818000007824

Author: Stewart

Publisher: CENGAGE L

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Chapter 10.3, Problem 36E

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To find:

The partial fraction decomposition of the rational function 3x2+12x−20x4−8x2+16.

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Chapter 10.3, Problem 35E

Chapter 10.3, Problem 37E

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Ch. 10.1 - CONCEPTS The system of equations {2x+3y=75xy=9 is...Ch. 10.1 - CONCEPTS A system of equations in two variables...Ch. 10.1 - Prob. 3E Ch. 10.1 - Prob. 4E Ch. 10.1 - Prob. 5E Ch. 10.1 - Prob. 6E Ch. 10.1 - SKILLS 58 Substitution Method Use the...Ch. 10.1 - Prob. 8E Ch. 10.1 - Prob. 9E Ch. 10.1 - Prob. 10E

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The partial fraction decomposition of the rational function 3 x 2 + 12 x − 20 x 4 − 8 x 2 + 16 .

Solution Summary: The author explains that the partial tion decomposition of the rational function is 1(x-2)+

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To find:

The partial fraction decomposition of the rational function 3x2+12x−20x4−8x2+16.

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Chapter 10 Solutions

The partial fraction decomposition of the rational function 3 x 2 + 12 x − 20 x 4 − 8 x 2 + 16 .

Solution Summary: The author explains that the partial tion decomposition of the rational function is 1(x-2)+

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To find: The partial fraction decomposition of the rational function 3x2+12x−20x4−8x2+16.

Want to see the full answer?

Chapter 10 Solutions

To find:

The partial fraction decomposition of the rational function 3x2+12x−20x4−8x2+16.