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 - 7.4 Adding and Subtracting Rational Expressions - 7.4 Exercises - Page 589: 34

Answer

$ \frac{5x+32}{x+4}$

Work Step by Step

Given \begin{equation} 8-\frac{3 x}{x+4}. \end{equation} First rewrite $8$ as a fraction: \begin{equation} 8= 8\cdot\frac{x+4}{x+4}= \frac{8x+32}{x+4}. \end{equation} Find the LCD of the fractions which is: $\mathbf{LCD}=x+4$. Perform subtraction: \begin{equation} \begin{aligned} 8-\frac{3 x}{x+4}&=\frac{8x+32}{x+4}-\frac{3 x}{x+4} \\ &= \frac{5x+32}{x+4}. \end{aligned} \end{equation}
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