Algebra: A Combined Approach (4th Edition)

Published by Pearson

Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set - Page 516: 57

Answer

$\dfrac{x+8}{x^{2}-5x-6}+\dfrac{x+1}{x^{2}-4x-5}=\dfrac{2(x^{2}-x-23)}{(x+1)(x-6)(x-5)}$

Work Step by Step

$\dfrac{x+8}{x^{2}-5x-6}+\dfrac{x+1}{x^{2}-4x-5}$ Factor the denominator of both rational expressions: $\dfrac{x+8}{x^{2}-5x-6}+\dfrac{x+1}{x^{2}-4x-5}=\dfrac{x+8}{(x-6)(x+1)}+\dfrac{x+1}{(x-5)(x+1)}$ Evaluate the sum of the two rational expressions and simplify: $...=\dfrac{(x+8)(x-5)+(x+1)(x-6)}{(x+1)(x-6)(x-5)}=...$ $...=\dfrac{x^{2}+3x-40+x^{2}-5x-6}{(x+1)(x-6)(x-5)}=\dfrac{2x^{2}-2x-46}{(x+1)(x-6)(x-5)}=...$ Take out common factor $2$ from the numerator to provide a more simplified answer: $...=\dfrac{2(x^{2}-x-23)}{(x+1)(x-6)(x-5)}$

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