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Chapter 11: Q. 24 (page 796)

In Problems 24and 25, write the partial fraction decomposition of each rational expression.

3x+7(x+3)2

Short Answer

Expert verified

The decomposition fraction is3x+7(x+3)2=3x+3-2(x+3)2

Step by step solution

01

Step 1. Given information

An expression is given as3x+7(x+3)2

02

Step 2. Partial fraction decomposition

Decompose the rational fraction as,

3x+7(x+3)2=Ax+3+B(x+3)2

Now simplify,

3x+7=A(x+3)+B=Ax+B+3A

Now, this is an identity. We equate the coefficients in power of x.

3=A7=3A+B

Now from above set we conclude that A=3&B=-2

After substituting the values of Aand B ,we get

3x+7(x+3)2=3x+3-2(x+3)2

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