   Chapter 7.4, Problem 4E

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) x 4 − 2 x 3 + x 2 + 2 x − 1 x 2 − 2 x + 1 (b) x 2 − 1 x 3 + x 2 + x

To determine

a) To decompose the function as partial fractions x42x3+x2+2x1x22x+1

Explanation

Calculation: Given x42x3+x2+2x1x22x+1

The denominator can be further decomposed as it is factorable

x22x+1=(x1)2

x42x3+x2+2x1x22x+1=x2(x22x+1)+2x1x22x+1=x2(x22x+1)x22x+1+2x1x22x+1=x2+2x1x22x+1

Therefore

x42x3+x2+2x

To determine

b) To decompose the function as partial fractions x21x3+x2+x

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