Algebra: A Combined Approach (4th Edition)

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

Chapter 7 - Section 7.7 - Simplifying Complex Fractions - Exercise Set: 21

Answer

$\dfrac{1+\dfrac{1}{y-2}}{y+\dfrac{1}{y-2}}=\dfrac{1}{y-1}$

Work Step by Step

$\dfrac{1+\dfrac{1}{y-2}}{y+\dfrac{1}{y-2}}$ Evaluate the sums indicated in the numerator and in the denominator: $\dfrac{1+\dfrac{1}{y-2}}{y+\dfrac{1}{y-2}}=\dfrac{\dfrac{y-2+1}{y-2}}{\dfrac{y(y-2)+1}{y-2}}=\dfrac{\dfrac{y-1}{y-2}}{\dfrac{y^{2}-2y+1}{y-2}}=...$ Evaluate the division: $...=\dfrac{y-1}{y-2}\div\dfrac{y^{2}-2y+1}{y-2}=\dfrac{(y-1)(y-2)}{(y^{2}-2y+1)(y-2)}=...$ $...=\dfrac{y-1}{y^{2}-2y+1}=...$ Factor the denominator, which is a perfect square trinomial, and simplify: $...=\dfrac{y-1}{(y-1)^{2}}=\dfrac{1}{y-1}$
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