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: 59



Work Step by Step

$\dfrac{5}{4n^{2}-12n+8}-\dfrac{3}{3n^{2}-6n}$ Factor the denominator of the first fraction and take out common factor $3n$ from the denominator of the second fraction: $\dfrac{5}{4n^{2}-12n+8}-\dfrac{3}{3n^{2}-6n}=\dfrac{5}{4(n-1)(n-2)}-\dfrac{3}{3n(n-2)}=...$ Evaluate the substraction of the two rational expressions: $...=\dfrac{5(3n)-3(4)(n-1)}{(4)(3n)(n-1)(n-2)}=\dfrac{15n-12n+12}{12n(n-1)(n-2)}=...$ $...=\dfrac{3n+12}{12n(n-1)(n-2)}=...$ Take out common factor $3$ from the numerator and simplify: $...=\dfrac{3(n+4)}{12n(n-1)(n-2)}=\dfrac{n+4}{4n(n-1)(n-2)}$
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