#### 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:
$...=\dfrac{(m+2)(m-2)(m+2)}{2(m-2)(m+2)}=\dfrac{m+2}{2}$