Introductory Algebra for College Students (7th Edition)

Published by Pearson
ISBN 10: 0-13417-805-X
ISBN 13: 978-0-13417-805-9

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Exercise Set - Page 498: 10



Work Step by Step

Step by step multiplication of rational expressions: 1. Factor completely what you can 2. Reduce (divide) numerators and denominators by common factors. 3. Multiply the remaining factors in the numerators and multiply the remaining factors in the denominators. $(\displaystyle \frac{P}{Q}\cdot\frac{R}{S}=\frac{PR}{QS})$ --- Factor what we can: $x^{2}+9x+18=...$ ... factor the trinomial $x^{2}+bx+c$ ... by searching for two factors of $c$ whose sum is $b$. ... Here, we find that $6$ and $3 $are factors of $18$ whose sum is $9.$ $=(x+3)(x+6)$ The problem becomes $...=\displaystyle \frac{(x+3)(x+6)\cdot 1}{(x+6)\cdot(x+3)}\qquad $... divide out the common factors $=\displaystyle \frac{1}{1}$ = $1$
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