Answer
$\frac{3m^2+2m-12}{5(m+2)}$
Work Step by Step
Multiply $m^2-4=(m-2)(m+2)$ to both the numerator and the denominator, we have
$\frac{3+\frac{2m}{m^2-4}}{\frac{5}{m-2}}=\frac{3+\frac{2m}{m^2-4}}{\frac{5}{m-2}}\times\frac{m^2-4}{m^2-4}=\frac{3m^2-12+2m}{5(m+2)}=\frac{3m^2+2m-12}{5(m+2)}$
