Answer
$\frac{m^3-4m-1}{m-2}$
Work Step by Step
Step 1. Perform operations to the numerator:
$m-\frac{1}{m^2-4}=\frac{m^3-4m-1}{m^2-4}=\frac{m^3-4m-1}{(m+2)(m-2)}$
Step 2. Use the above result in the original expression, we have:
$\frac{m-\frac{1}{m^2-4}}{\frac{1}{m+2}}=\frac{\frac{m^3-4m-1}{(m+2)(m-2)}}{\frac{1}{m+2}}=\frac{m^3-4m-1}{(m+2)(m-2)}\cdot \frac{m+2}{1}=\frac{m^3-4m-1}{m-2}$
