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 7.1 - Rational Expressions and Their Simplification - Exercise Set - Page 492: 81


$\displaystyle \frac{y+3}{x+3}$

Work Step by Step

1. Factor the numerator and the denominator completely. 2. Divide both the numerator and the denominator by any common factors. --- Numerator $:$ factor in pairs $xy+2y+3x+6=y(x+2)+3(x+2)=(y+3)(x+2)$ Denominator: search for integer factors of $6$ whose sum is $5$... ... these are $2$ and $3...$ $ x^{2}+5x+6=(x+2)(x+3)$ Expression = $\displaystyle \frac{(y+3)(x+2)}{(x+2)(x+3)}$ ... divide both with the common factor: $(x+2)$ Expression = $\displaystyle \frac{y+3}{x+3}$
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