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Chapter 11: Q. 49 (page 765)

Use the division algorithm to rewrite each improper fraction as the sum of a quotient and proper fraction. Find the partial fraction decomposition of the proper fraction. Finally, express the improper fraction as the sum of a quotient and the partial fraction decomposition.

x3x2+1

Short Answer

Expert verified

x3x2+1=x-xx2+1

Step by step solution

01

Step 1. Given information.

Improper fractionx3x2+1

02

Express in partial fraction decomposition.

First, we have to convert the improper fraction as the sum of a quotient and a proper fraction.

x3x2+1=x-xx2+1

Now, find the partial fraction of the second term.

xx2+1=Ax+Bx2+1x=Ax+B

After comparing the coefficient of variable and constant.

We get that,

A=1,B=0

Therefore,

xx2+1=xx2+1

So that, given improper fraction can be written as,

x3x2+1=x-xx2+1

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