Simplify Rational Expressions: example 8.13

$\begin{array}{cccc}& & & \hfill \frac{m^3+8}{m^2-4}\hfill \\ \begin{array}{c}\text{Factor the numerator and denominator,}\hfill \\ \text{using the formulas for sum of cubes and}\hfill \\ \text{difference of squares.}\hfill \end{array}\hfill & & & \hfill \frac{\left(m+2\right)\left(m^2-2m+4\right)}{\left(m+2\right)\left(m-2\right)}\hfill \\ \text{Remove the common factor of}m+2.\hfill & & & \hfill \frac{\cancel{\left(m+2\right)}\left(m^2-2m+4\right)}{\cancel{\left(m+2\right)}\left(m-2\right)}\hfill \\ & & & \hfill \frac{m^2-2m+4}{m-2}\hfill \end{array}$