Intermediate Algebra: Connecting Concepts through Application

Published by Brooks Cole
ISBN 10: 0-53449-636-9
ISBN 13: 978-0-53449-636-4

Chapter 7 - Rational Functions - 7.1 Rational Functions and Variation - 7.1 Exercises: 39

Answer

$\text{all real numbers except }$ $ m=\left\{ -4,-3 \right\}$

Work Step by Step

$\bf{\text{Solution Outline:}}$ The domain of the given rational function, $ h(m)=\dfrac{4m^2+2m-9}{m^2+7m+12} ,$ are the values of $ m $ which will NOT make the denominator equal to $0.$ $\bf{\text{Solution Details:}}$ The values of $ m $ that will make the denominator equal to $0$ are \begin{array}{l}\require{cancel} m^2+7m+12=0 .\end{array} Using the FOIL Method, which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the equation above is equivalent to \begin{array}{l}\require{cancel} (m+3)(m+4)=0 .\end{array} Equating each factor to zero (Zero Product Property), then \begin{array}{l}\require{cancel} m+3=0 \\\\\text{OR}\\\\ m+4=0 .\end{array} Solving each equation results to \begin{array}{l}\require{cancel} m+3=0 \\\\ m=-3 \\\\\text{OR}\\\\ m+4=0 \\\\ m=-4 .\end{array} Hence, the domain is the set of $ \text{all real numbers except }$ $ m=\left\{ -4,-3 \right\} .$
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