College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter P, Prerequisites - Section P.7 - Rational Expressions - P.7 Exercises: 75

Answer

$-\frac{2x+h}{x^{2}(x+h)^{2}}$

Work Step by Step

We form a common denominator for the top fractions, then simplify: $\displaystyle \frac{\frac{1}{(x+h)^{2}}-\frac{1}{x^{2}}}{h}=\frac{x^{2}-(x+h)^{2}}{hx^{2}(x+h)^{2}}=\frac{x^{2}-(x^{2}+2xh+h^{2})}{hx^{2}(x+h)^{2}}=-\frac{2x+h}{x^{2}(x+h)^{2}}$
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