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: 55

Answer

$\dfrac{70}{m^{2}-100}+\dfrac{7}{2(m+10)}=\dfrac{7}{2(m-10)}$

Work Step by Step

$\dfrac{70}{m^{2}-100}+\dfrac{7}{2(m+10)}$ Factor the denominator of the first fraction: $\dfrac{70}{m^{2}-100}+\dfrac{7}{2(m+10)}=\dfrac{70}{(m-10)(m+10)}+\dfrac{7}{2(m+10)}=...$ Evaluate the sum of the two rational expressions and simplify: $...=\dfrac{70(2)+7(m-10)}{2(m+10)(m-10)}=\dfrac{140+7m-70}{2(m+10)(m-10)}=...$ $...=\dfrac{7m+70}{2(m+10)(m-10)}=...$ Take out common factor $7$ from the numerator to provide a more simplified answer: $...=\dfrac{7(m+10)}{2(m+10)(m-10)}=\dfrac{7}{2(m-10)}$
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