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 6.2 - Adding and Subtracting Rational Expressions - Exercise Set - Page 427: 46


$\displaystyle \frac{x^{2}+x+4}{(x-6)(x-1)(x+1)}$

Work Step by Step

1. Find the LCD . 1st denominator = $(x-6)(x-1)$ 2nd denominator = $(x-6)(x+1)$ List factors of the 1st denominator. From each next denominator, add only those factors that do not yet appear in the list. LCD = $(x-6)(x-1)(x+1)$ 2. Rewrite each rational expression with the the LCDas the denominator = $\displaystyle \frac{(2x+1)(x+1)}{(x-6)(x-1)(x+1)}-\frac{(x+3)(x-1)}{ (x-6)(x+1)(x-1)}$ 3. Add or subtract numerators, placing the resulting expression over the LCD. = $\displaystyle \frac{(2x+1)(x+1)-(x+3)(x-1)}{(x-6)(x-1)(x+1)}$ 4. If possible, simplify. = $\displaystyle \frac{2x^{2}+2x+x+1-(x^{2}+3x-x-3)}{(x-6)(x-1)(x+1)} $ = $\displaystyle \frac{2x^{2}+2x+x+1-x^{2}-3x+x+3}{(x-6)(x-1)(x+1)} $ = $\displaystyle \frac{x^{2}+x+4}{(x-6)(x-1)(x+1)}$
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