Question

In Problems 13-46, write the partial fraction decomposition of each rational expression. $\frac{x^2-x-8}{(x+1)\left(x^2+5 x+6\right)}$

   In Problems 13-46, write the partial fraction decomposition of each rational expression.
 $\frac{x^2-x-8}{(x+1)\left(x^2+5 x+6\right)}$

Precalculus: pearson new international edition

Precalculus: pearson new international edition

Michael Sullivan 9th Edition

Chapter 11, Problem 34

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Step 1

The denominator given is \((x+1)(x^2+5x+6)\). We notice that \(x^2+5x+6\) can be further factorized. To factorize \(x^2+5x+6\), we look for two numbers that multiply to 6 and add up to 5. These numbers are 2 and 3. Therefore, \(x^2+5x+6\) can be factorized as Show more…

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In Problems 13-46, write the partial fraction decomposition of each rational expression. $\frac{x^2-x-8}{(x+1)\left(x^2+5 x+6\right)}$

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