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: 35


$\displaystyle \frac{2x^{2}-2x+61}{(x+5)(x-6)}$

Work Step by Step

1. Find the LCD . LCD = $(x+5)(x-6)$ 2. Rewrite each rational expression with the the LCD as the denominator = $\displaystyle \frac{(x-6)(x-6)}{(x+5)(x-6)}+\frac{(x+5)(x+5)}{(x-6)(x+5)}$ 3. Add or subtract numerators, placing the resulting expression over the LCD. = $\displaystyle \frac{(x-6)^{2}+(x+5)^{2}}{(x+5)(x-6)}$ 4. If possible, simplify. = $\displaystyle \frac{x^{2}-12x+36+x^{2}+10x+25}{(x+5)(x-6)} $ = $\displaystyle \frac{2x^{2}-2x+61}{(x+5)(x-6)}$ The numerator is of 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 $122$ whose sum is $-2$ ... we can't factor the numerator, so we leave it as it is.
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