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: 44

Answer

$\displaystyle \frac{7x^{2}+12x-12}{(x-3)(x+2)(x+3)}$

Work Step by Step

1. Find the LCD . 1st denominator = $(x-3)(x+2)$ 2nd denominator = $(x-3)(x+3)$ List factors of the 1st denominator. From each next denominator, add only those factors that do not yet appear in the list. LCD = $(x-3)(x+2)(x+3)$ 2. Rewrite each rational expression with the the LCDas the denominator = $\displaystyle \frac{(3x-2)(x+3)}{(x-3)(x+2)(x+3)}+\frac{(4x-3)(x+2)}{(x-3)(x+3)(x+2)}$ 3. Add or subtract numerators, placing the resulting expression over the LCD. = $\displaystyle \frac{(3x-2)(x+3)+(4x-3)(x+2)}{(x-3)(x+2)(x+3)}$ 4. If possible, simplify. = $\displaystyle \frac{3x^{2}+9x-2x-6+4x^{2}+8x-3x-6}{(x-3)(x+2)(x+3)} $ = $\displaystyle \frac{7x^{2}+12x-12}{(x-3)(x+2)(x+3)}$ The numerator has the form $ax^{2}+bx+c.$ To factor, find factors of $ac$ whose sum is $b.$ If successful, rewrite $bx$ and factor in pairs. ... we can't find factors of $-84$ whose sum is $+12$ ... we can't factor the numerator, so we leave it as is.
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.