## Intermediate Algebra for College Students (7th Edition)

Published by Pearson

# Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set - Page 427: 40

#### Answer

$\displaystyle \frac{17}{(y-3)(y-4)}$

#### Work Step by Step

1. Find the LCD . 1st denominator = $(y-3)(x-4)$ 2nd denominator = $(y-3)$ List factors of the 1st denominator. From each next denominator, add only those factors that do not yet appear in the list. LCD = $(y-3)(y-4)$ 2. Rewrite each rational expression with the the LCDas the denominator = $\displaystyle \frac{2y+9}{(y-3)(y-4)}-\frac{2(y-4)}{(y-3)(y-4)}$ 3. Add or subtract numerators, placing the resulting expression over the LCD. = $\displaystyle \frac{2y+9-2(y-4)}{(y-3)(y-4)}$ 4. If possible, simplify. = $\displaystyle \frac{2y+9-2y+8}{(y-3)(y-4)}$ = $\displaystyle \frac{17}{(y-3)(y-4)}$

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