Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter R - Elementary Algebra Review - R.6 Rational Expressions and Equations - R.6 Exercise Set - Page 980: 22


The simplified form of the expression $\frac{2x}{x-5}+\frac{3}{x+4}$ is $\frac{2{{x}^{2}}+11x-15}{\left( x+4 \right)\left( x-5 \right)}$ .

Work Step by Step

$\frac{2x}{x-5}+\frac{3}{x+4}$ Solve to obtain the LCD of the denominator of the fractions that is $\left( x-5 \right)$ and $\left( x+4 \right)$. On solving the LCD is $\left( x-5 \right)\left( x+4 \right)$. The rational expression is written as a fraction in such a way that the LCD is the denominator of the fraction. Consider, the individual terms of the provided rational terms; $\frac{2x}{x-5}=\frac{\left( 2x \right)\left( x+4 \right)}{\left( x-5 \right)\left( x+4 \right)}$ And, $\frac{3}{x+4}=\frac{3\left( x-5 \right)}{\left( x-5 \right)\left( x+4 \right)}$ Since the fractions have a common denominator, add the numerators and the LCD is the denominator: $\begin{align} & \frac{2x}{x-5}+\frac{3}{x+4}=\frac{\left( 2x \right)\left( x+4 \right)}{\left( x-5 \right)\left( x+4 \right)}+\frac{3\left( x-5 \right)}{\left( x-5 \right)\left( x+4 \right)} \\ & =\frac{\left( 2x \right)\left( x+4 \right)+3\left( x-5 \right)}{\left( x-5 \right)\left( x+4 \right)} \end{align}$ Solve the above expression as: $\begin{align} & \frac{2x}{x-5}+\frac{3}{x+4}=\frac{2{{x}^{2}}+8x+3x-15}{\left( x-5 \right)\left( x+4 \right)} \\ & =\frac{2{{x}^{2}}+11x-15}{\left( x-5 \right)\left( x+4 \right)} \end{align}$
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