College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 5, Systems of Equations and Inequalities - Section 5.3 - Partial Fractions - 5.3 Exercises - Page 461: 10

Answer

$\dfrac{A}{x}+\dfrac{B}{x^2}+\dfrac{Cx+D}{x^2+4}+\dfrac{Ex+F}{(x^2+4)^2}$

Work Step by Step

Simplify $\dfrac{x^4+x^2+1}{x^2(x^2+4)^2}$ into partial fraction decomposition. Here, the denominator terms can be be further factorized.Thus, the partial decomposition will be shown in a linear function of $x$. Applying the partial fraction decomposition rule. $\dfrac{x^4+x^2+1}{x^2(x^2+4)^2}=\dfrac{A}{x}+\dfrac{B}{x^2}+\dfrac{Cx+D}{x^2+4}+\dfrac{Ex+F}{(x^2+4)^2}$
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