Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter P - Section P.6 - Rational Expressions - Concept and Vocabulary Check - Page 84: 10

Answer

first blank $\rightarrow \ \ x-(x+3)$ second blank $\rightarrow \ \ -3$ third blank $\rightarrow\ \ -\displaystyle \frac{1}{x(x+3)}$

Work Step by Step

The complex rational expression is multiplied with $\displaystyle \frac{x(x+3)}{x(x+3)}=1$ in order to cancel the fractions in the numerator After this, the numerator equals $\underbrace{x}_{(x+3)\ cancels} - \underbrace{(x+3)}_{x\ cancels}$ we fill the first blank with $x-(x+3)$ After simplifying the numerator, it equals $-3$. The expression is now $=-\displaystyle \frac{3}{3x(x+3)}\qquad $... fill the second blank with $-3$. 3 is a common factor, so we reduce (divide both the numerator and denominator) with 3 $=-\displaystyle \frac{1}{x(x+3)}\qquad $... third blank = $-\displaystyle \frac{1}{x(x+3)}$
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