Explanation Given: The rational expression is 4 x 3 + 5 x 2 + 7 x - 1 ( x 2 + x + 1 ) 2 Calculation: Factor the denominator by the method of grouping as the expression x 2 + x + 1 occurs multiple times in the denominator of the rational expression, so, for each power of x 2 + x + 1 assign an undefined constant shown below: 4 x 3 + 5 x 2 + 7 x - 1 ( x 2 + x + 1 ) 2 = A x + B x 2 + x + 1 + C x + D ( x 2 + x + 1 ) 2 Multiply both sides by ( x 2 + x + 1 ) 2 as shown below: 4 x 3 + 5 x 2 + 7 x - 1 = ( A x + B ) ( x 2 + x + 1 ) + C x + D 4 x 3 + 5 x 2 + 7 x - 1 = A x 3 + A x 2 + A x + B x 2 + B x + B + C x + D 4 x 3 + 5 x 2 + 7 x - 1 = A x 3 + ( A + B ) x 2 + ( A + B + C ) x + ( B + D )

5th Edition

ISBN: 9780321837240

Author: Robert F. Blitzer

Publisher: PEARSON

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Chapter 8, Problem 24RE

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To calculate: The partial fraction decomposition of the rational expression

4x3+5x2+7x-1(x2+x+1)2

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Chapter 8, Problem 23RE

Chapter 8, Problem 25RE

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The partial fraction decomposition of the rational expression 4 x 3 + 5 x 2 + 7 x - 1 ( x 2 + x + 1 ) 2

Solution Summary: The author calculates the partial tion decomposition of the rational expression x2+x+1 by the method of grouping.

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To calculate: The partial fraction decomposition of the rational expression

4x3+5x2+7x-1(x2+x+1)2

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Chapter 8 Solutions

The partial fraction decomposition of the rational expression 4 x 3 + 5 x 2 + 7 x - 1 ( x 2 + x + 1 ) 2

Solution Summary: The author calculates the partial tion decomposition of the rational expression x2+x+1 by the method of grouping.

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To calculate: The partial fraction decomposition of the rational expression 4x3+5x2+7x-1(x2+x+1)2

Want to see the full answer?

Chapter 8 Solutions

To calculate: The partial fraction decomposition of the rational expression

4x3+5x2+7x-1(x2+x+1)2