Finite Math and Applied Calculus (6th Edition)

Published by Brooks Cole
ISBN 10: 1133607705
ISBN 13: 978-1-13360-770-0

Chapter 0 - Section 0.4 - Rational Expressions - Exercises - Page 23: 15

Answer

$$ - \frac{{2x + y}}{{{x^2}{{\left( {x + y} \right)}^2}}}$$

Work Step by Step

$$\eqalign{ & \frac{{\frac{1}{{{{\left( {x + y} \right)}^2}}} - \frac{1}{{{x^2}}}}}{y} \cr & {\text{Subtract fractions in the numerator}} \cr & = \frac{{\frac{{{x^2} - {{\left( {x + y} \right)}^2}}}{{{x^2}{{\left( {x + y} \right)}^2}}}}}{y} \cr & = \frac{{\frac{{{x^2} - {x^2} - 2xy - {y^2}}}{{{x^2}{{\left( {x + y} \right)}^2}}}}}{y} \cr & = \frac{{\frac{{ - 2xy - {y^2}}}{{{x^2}{{\left( {x + y} \right)}^2}}}}}{y} = \frac{{ - 2xy - {y^2}}}{{{x^2}y{{\left( {x + y} \right)}^2}}} \cr & {\text{Simplify}} \cr & = \frac{{ - 2x - y}}{{{x^2}{{\left( {x + y} \right)}^2}}} \cr & = - \frac{{2x + y}}{{{x^2}{{\left( {x + y} \right)}^2}}} \cr} $$
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