   Chapter 7.4, Problem 6E

Chapter
Section
Textbook Problem

# Write out the form of the partial fraction decomposition of the function (as in Example 7). Do not determine the numerical values of the coefficients.(a) t 6 + 1 t 6 + t 3 (b) x 5 + 1 ( x 2 − x ) ( x 4 + 2 x 2 + 1 )

To determine

a) To decompose the function as partial fractions t6+1t6t3

Explanation

Calculation: Given t6+1t6t3

Since the degree of the numerator is same the degree of denominator, this enables to write

Therefore t6+1=(t6t3)(1) + (-t3+1)

t6+1t6t3=1+t3+1t3(t31)

Decomposition of the denominator termgives

(t6t3)=t3(t31)=t3(t1)(t2+t+1)

t6+1t6<

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