   Chapter 8.5, Problem 4E

Chapter
Section
Textbook Problem

# Partial Fraction Decomposition Write the form of the partial fraction decomposition of each rational expression. Do not solve for the constants.(a) 4 x 2 − 8 x (b) 2 x 2 − 1 ( x − 3 ) 3 (c) 2 x − 3 x 3 + 10 x (d) 2 x − 1 x ( x 2 + 1 ) 2

(a)

To determine

To calculate: The partial fraction decomposition form of the rational expression 4x28x.

Explanation

Given:

The rational expression, 4x28x

Formula used:

For each factor of form (px+q)m, the partial fraction decomposition must include the following sum of m fractions.

A1(px+q)+A2(px+q)2++Am(px+q)m

Calculation:

Consider the rational expression,

<

(b)

To determine

To calculate: The partial fraction decomposition form of the rational expression 2x2+1(x3)3.

(c)

To determine

To calculate: The partial fraction decomposition form of the rational expression 2x3x3+10x.

(d)

To determine

To calculate: The partial fraction decomposition form of the rational expression 2x1x(x2+1)2.

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