College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter R - Section R.7 - Rational Expressions - R.7 Assess Your Understanding - Page 70: 13


$\dfrac{y+5}{2(y+1)}; y\ne-1, 5$

Work Step by Step

Factor the numerator and the denominator completely to obtain: $=\dfrac{(y-5)(y+5)}{2(y^2-4y-5)} \\=\dfrac{(y-5)(y+5)}{2(y-5)(y+1)}$ Cancel the common factors to obtain: $\require{cancel} \\=\dfrac{\cancel{(y-5)}(y+5)}{2\cancel{(y-5)}(y+1)} \\=\dfrac{y+5}{2(y+1)}; y\ne-1, 5$ ($y$ cannot be $-1$ and $5$ because they will make the original expression undefined.)
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