Intermediate Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-894-7
ISBN 13: 978-0-13417-894-3

Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set - Page 429: 84

Answer

$ \frac{2x(2x+9)}{(x+4)(x+5)} $.

Work Step by Step

The perimeter of the rectangle is $=2(sum\; of \; the \;sides)$. The given sides of the rectangle are: $\Rightarrow \frac{x}{x+5}$ and $\frac{x}{x+4}$ Thus, the perimeter of the rectangle is: $\Rightarrow 2\left ( \frac{x}{x+5}+\frac{x}{x+4} \right )$ Factor out $x$. $\Rightarrow 2x\left ( \frac{1}{x+5}+\frac{1}{x+4} \right )$ The LCD of the denominators is $(x+5)(x+4)$. Multiply both the numerator and the denominator: $\Rightarrow 2x\left ( \frac{x+4}{(x+4)(x+5)}+\frac{x+5}{(x+4)(x+5)} \right )$ Add both the numerators because denominators are equal. $\Rightarrow 2x\left ( \frac{x+4+x+5}{(x+4)(x+5)} \right )$ Simplify. $\Rightarrow 2x\left ( \frac{2x+9}{(x+4)(x+5)} \right )$ $\Rightarrow \frac{2x(2x+9)}{(x+4)(x+5)} $.
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