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 6.1 - Rational Expressions and Functions; Multiplying and Dividing - Exercise Set - Page 414: 53


$\frac{x+7}{x}$ and $x\ne7, x\ne-3.$

Work Step by Step

The product of a binomial sum and a binomial difference is: $(A+B)(A-B)=A^2-B^2$. Hence: $\frac{x^2-49}{x^2-4x-21}\frac{x+3}{x}=\frac{x^2-7^2}{x^2+3x-7x-21}\frac{x+3}{x}=\frac{(x+7)(x-7)}{x(x+3)-7(x+3)}=\frac{(x+7)(x-7)}{(x+3)(x-7)}\frac{x+3}{x}=\frac{x+7}{x}$ and $x\ne7, x\ne-3.$
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