algebra

Factor out\(8m^2+16m\) to get\(8m(m+2)\).

Factor out\(m^2-m-6\) to get\((m+2)(m-3)\).

Factor out\(4m^3+8m^2\) to get\(4m^2(m+2)\).

 

\(\frac{8m(m+2)}{m-3}\times\frac{(m+2)(m-3)}{4m^2(m+2)}\).

 

"Crossing off" \(4m(m+2)\) we get \(\frac{2}{m-3}\times\frac{(m+2)(m-3)}{m}\)

"Crossing off" \(m-3\) we get \(2\times\frac{m+2}{m}\)

 

Solving, we get \(\frac{2m+4}{m}\).

 

You are very welcome!
:P