Intermediate Algebra for College Students (7th Edition)

Published by Pearson

Chapter 6 - Section 6.2 - Adding and Subtracting Rational Expressions - Exercise Set - Page 427: 36

Answer

$\displaystyle \frac{2x^{2}+10x+53}{(x+7)(x-2)}$

Work Step by Step

1. Find the LCD . LCD = $(x+7)(x-2)$ 2. Rewrite each rational expression with the the LCDas the denominator = $\displaystyle \frac{(x-2)(x-2)}{(x+7)(x-2)}+\frac{(x+7)(x+7)}{(x+7)(x-2)}$ 3. Add or subtract numerators, placing the resulting expression over the LCD. = $\displaystyle \frac{(x-2)^{2}+(x+7)^{2}}{(x+7)(x-2)}$ 4. If possible, simplify. = $\displaystyle \frac{x^{2}-4x+4+x^{2}+14x+49}{(x+7)(x-2)}$ = $\displaystyle \frac{2x^{2}+10x+53}{(x+7)(x-2)}$ 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 $106$ whose sum is $+10$ ... we can't factor the numerator, so we leave it as it is.

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