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: 60

Answer

$\dfrac{6}{5y^{2}-25y+30}-\dfrac{2}{4y^{2}-8y}=\dfrac{7y+15}{10y(y-3)(y-2)}$

Work Step by Step

$\dfrac{6}{5y^{2}-25y+30}-\dfrac{2}{4y^{2}-8y}$ Take out common factor $5$ from the denominator of the first fraction and common factor $4y$ from the denominator of the second fraction: $\dfrac{6}{5y^{2}-25y+30}-\dfrac{2}{4y^{2}-8y}=\dfrac{6}{5(y^{2}-5y+6)}-\dfrac{2}{4y(y-2)}=...$ Factor the expression inside the parentheses in the denominator of the first fraction: $...=\dfrac{6}{5(y-3)(y-2)}-\dfrac{2}{4y(y-2)}=...$ Evaluate the substraction of the two rational expressions: $...=\dfrac{6(4y)-2(5)(y-3)}{(5)(4y)(y-3)(y-2)}=\dfrac{24y-10y+30}{20y(y-3)(y-2)}=...$ $...=\dfrac{14y+30}{20y(y-3)(y-2)}=...$ Take out common factor $2$ from the numerator and simplify: $...=\dfrac{2(7y+15)}{20y(y-3)(y-2)}=\dfrac{7y+15}{10y(y-3)(y-2)}$
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