Intermediate Algebra (6th Edition)

Published by Pearson
ISBN 10: 0321785045
ISBN 13: 978-0-32178-504-6

Chapter 6 - Section 6.3 - Simplifying Complex Fractions - Exercise Set - Page 362: 76

Answer

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

Work Step by Step

For part a, replace wherever you see an x with a+h. This gives: $$ \frac{2}{(a+h)^2}$$ For part b, replace wherever you see an x with a. This gives: $$ \frac{2}{a^2}$$ Now, we are asked to plug the answers from a and b into the equation: $$ \frac {f(a+h)-f(a)}{h}$$ We substitute to find: $$\frac{\frac{2}{(a+h)^2} - \frac{2}{a^2}}{h}$$ Lastly, we simplify using the techniques learned in this chapter. This gives: $$ - \frac{2(2a+h)}{a^2(a+h)^2}$$
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