Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.2 - Multiplying and Dividing Rational Expressions - Practice: 8


a. $\frac{7}{x}$ b. $\frac{(x+3)^2}{7x}$ c. $-\frac{2}{(x+1)(x-4)}$

Work Step by Step

a. $\frac{x+3}{x} \times \frac{7}{x+3}$ $\frac{(x+3)7}{x(x+3)}$ $=\frac{7}{x}$ b. $\frac{x+3}{x} \div \frac{7}{x+3}$ $=\frac{x+3}{x} \times \frac{x+3}{7}$ $=\frac{(x+3)(x+3)}{x(7)}$ $=\frac{(x+3)^2}{7x}$ c. $\frac{3-x}{x^2+6x+5} \times \frac{2x+10}{x^2-7x+12}$ $=\frac{3-x}{(x+1)(x+5)} \times \frac{2(x+5)}{(x-3)(x-4)}$ $=\frac{-(x-3)}{(x+1)(x+5)} \times \frac{2(x+5)}{(x-3)(x-4)}$ $=\frac{-1}{(x+1)} \times \frac{2}{(x-4)}$ $=-\frac{2}{(x+1)(x-4)}$
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