Elementary and Intermediate Algebra: Concepts & Applications (6th Edition)

Published by Pearson
ISBN 10: 0-32184-874-8
ISBN 13: 978-0-32184-874-1

Chapter 6 - Rational Expressions and Equations - 6.3 Addition, Subtraction, and Least Common Denominators - 6.3 Exercise Set: 31

Answer

$\dfrac{y+2}{y-4}$

Work Step by Step

Subtracting the numerators and copying the denominator, the given expression, $ \dfrac{2y^2+3y}{y^2-7y+12}-\dfrac{y^2+4y+6}{y^2-7y+12} ,$ simplifies to \begin{array}{l}\require{cancel} \dfrac{2y^2+3y-(y^2+4y+6)}{y^2-7y+12} \\\\= \dfrac{2y^2+3y-y^2-4y-6}{y^2-7y+12} \\\\= \dfrac{y^2-y-6}{y^2-7y+12} \\\\= \dfrac{(y-3)(y+2)}{(y-4)(y-3)} \\\\= \dfrac{(\cancel{y-3})(y+2)}{(y-4)(\cancel{y-3})} \\\\= \dfrac{y+2}{y-4} .\end{array}
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