EXAMPLE Write out the form of the partial fraction decomposition of the function x³ + x? + 1 x(x – 1)(x² + x + 1)(x² + 1)³ SOLUTION x³ + x? + 1 x(x – 1)(x² + x + 1)(x² + 1)³ Сх + D Ex + F Ix + J B Gx + H x? + 1 (x² + 1)³ x? + x + 1 (x² + 1)² х

College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter7: Systems Of Equations And Inequalities
Section7.4: Partial Fractions
Problem 2SE: Can you explain why a partial fraction decomposition is unique? (Hint: Think about it as a system of...
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Question

Write out the form of the partial fraction decomposition of the function (as in this example). Do not determine the numerical values of the coefficients.

(a)    
x4 − 2x3 + x2 + 3x − 1
x2 − 2x + 1
EXAMPLE
Write out the form of the partial fraction decomposition of the function
x³ + x? + 1
x(x – 1)(x² + x + 1)(x² + 1)³
SOLUTION
x³ + x? + 1
x(x – 1)(x² + x + 1)(x² + 1)³
Сх + D
Ex + F
Ix + J
B
Gx + H
x? + 1
(x² + 1)³
x? + x + 1
(x² + 1)²
х
Transcribed Image Text:EXAMPLE Write out the form of the partial fraction decomposition of the function x³ + x? + 1 x(x – 1)(x² + x + 1)(x² + 1)³ SOLUTION x³ + x? + 1 x(x – 1)(x² + x + 1)(x² + 1)³ Сх + D Ex + F Ix + J B Gx + H x? + 1 (x² + 1)³ x? + x + 1 (x² + 1)² х
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