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 - Page 548: 20



Work Step by Step

$\dfrac{\dfrac{1}{y^{2}}+\dfrac{2}{3}}{\dfrac{1}{y}-\dfrac{5}{6}}$ Evaluate the sum indicated in the numerator and the substraction indicated in the denominator: $\dfrac{\dfrac{1}{y^{2}}+\dfrac{2}{3}}{\dfrac{1}{y}-\dfrac{5}{6}}=\dfrac{\dfrac{3+2y^{2}}{3y^{2}}}{\dfrac{6-5y}{6y}}=...$ Evaluate the division and simplify if possible: $...=\dfrac{3+2y^{2}}{3y^{2}}\div\dfrac{6-5y}{6y}=\dfrac{(3+2y^{2})(6y)}{(6-5y)(3y^{2})}=\dfrac{(2y^{2}+3)(2)}{(6-5y)(y)}=...$ $...=\dfrac{2(2y^{2}+3)}{y(6-5y)}$
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