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: 54

Answer

$\dfrac{-7}{y^{2}-3y+2}-\dfrac{2}{y-1}=-\dfrac{2y+3}{(y-2)(y-1)}$

Work Step by Step

$\dfrac{-7}{y^{2}-3y+2}-\dfrac{2}{y-1}$ Factor the denominator of the first fraction: $\dfrac{-7}{y^{2}-3y+2}-\dfrac{2}{y-1}=\dfrac{-7}{(y-2)(y-1)}-\dfrac{2}{y-1}=...$ Evaluate the substraction of the two rational expressions: $...=\dfrac{-7-2(y-2)}{(y-2)(y-1)}=\dfrac{-7-2y+4}{(y-2)(y-1)}=\dfrac{-2y-3}{(y-2)(y-1)}=...$ $...=-\dfrac{2y+3}{(y-2)(y-1)}$
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