Algebra: A Combined Approach (4th Edition)

Published by Pearson
ISBN 10: 0321726391
ISBN 13: 978-0-32172-639-1

Chapter 7 - Section 7.4 - Adding and Subtracting Rational Expressions with Different Denominators - Exercise Set: 17

Answer

$\dfrac{-8}{x^{2}-1}-\dfrac{7}{1-x^{2}}=\dfrac{1}{1-x^{2}}$

Work Step by Step

$\dfrac{-8}{x^{2}-1}-\dfrac{7}{1-x^{2}}$ Evaluate the substraction of the two rational expressions: $\dfrac{-8}{x^{2}-1}-\dfrac{7}{1-x^{2}}=\dfrac{-8(1-x^{2})-7(x^{2}-1)}{(x^{2}-1)(1-x^{2})}=...$ Change the sign of the denominator and the sign of the fraction: $...=-\dfrac{-8(1-x^{2})-7(x^{2}-1)}{(x^{2}-1)(x^{2}-1)}=-\dfrac{8(x^{2}-1)-7(x^{2}-1)}{(x^{2}-1)^{2}}=...$ $...=\dfrac{7(x^{2}-1)-8(x^{2}-1)}{(x^{2}-1)^{2}}=...$ Take out common factor $x^{2}-1$ from the numerator and simplify: $...=\dfrac{(x^{2}-1)(7-8)}{(x^{2}-1)^{2}}=-\dfrac{1}{x^{2}-1}=\dfrac{1}{1-x^{2}}$
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