Answer
$\text{The simplified form of the given complex fraction is } \dfrac{m^3-4m-1}{m-2}$.
Work Step by Step
$ \begin{array}{ l l }
=\dfrac{m-\dfrac{1}{( m+2)( m-2)}}{\dfrac{1}{m+2}} & \begin{array}{{l}}
\mathrm{Factor} \ m^{2} -4\ \mathrm{using\ the\ difference\ of\ }\\
\mathrm{two \space squares\ property} :( m+2)( m\ -\ 2)
\end{array}\\
& \\
=\dfrac{\left( m-\dfrac{1}{( m+2)( m-2)}\right) \cdot ( m+2)( m-2)}{\dfrac{1}{m+2} \cdot ( m+2)( m-2)} & \begin{array}{{l}}
\mathrm{Multiply\ the\ numerator\ and\ }\\
\mathrm{denominator\ of\ the\ complex\ }\\
\mathrm{fraction\ by\ the\ LCD\ which\ }\\
\mathrm{is} \ ( m+2)( m\ -\ 2).
\end{array}\\
& \\
=\dfrac{m( m+2)( m-2) -\dfrac{( m+2)( m-2)}{( m+2)( m-2)}}{\dfrac{m+2}{m+2} \cdot ( m-2)} & \begin{array}{{l}}
\mathrm{Apply\ the\ distributive\ property\ in\ }\\
\mathrm{the\ numerator} .\\
\mathrm{Apply\ the\ rule} \ a\cdot \dfrac{b}{c} =\dfrac{ab}{c}
\end{array}\\
& \\
=\dfrac{m( m+2)( m-2) -1}{1\cdot ( m-2)} & \mathrm{Apply\ the\ rule} \ \dfrac{a}{a} =1\\
& \\
=\dfrac{m\left( m^{2} -4\right) -1}{m-2} & \mathrm{Express} \ ( m+2)( m-2) \ \mathrm{as} \ m^{2} -4.\\
& \\
=\dfrac{m^{3} -4m-1}{m-2} & \mathrm{Apply\ the\ distributive\ property.}
\end{array}$
