## Algebra: A Combined Approach (4th Edition)

Published by Pearson

# Chapter 7 - Section 7.7 - Simplifying Complex Fractions - Exercise Set - Page 549: 30

#### Answer

$\dfrac{\dfrac{m+2}{m-2}}{\dfrac{2m+4}{m^{2}-4}}=\dfrac{m+2}{2}$

#### Work Step by Step

$\dfrac{\dfrac{m+2}{m-2}}{\dfrac{2m+4}{m^{2}-4}}$ Evaluate the division: $\dfrac{\dfrac{m+2}{m-2}}{\dfrac{2m+4}{m^{2}-4}}=\dfrac{m+2}{m-2}\div\dfrac{2m+4}{m^{2}-4}=\dfrac{(m+2)(m^{2}-4)}{(m-2)(2m+4)}=...$ Factor the second parentheses in the numerator and take out common factor $2$ from the second parentheses in the denominator and then simplify: $...=\dfrac{(m+2)(m-2)(m+2)}{2(m-2)(m+2)}=\dfrac{m+2}{2}$

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