First, we are going to simplify each rational expression:
[tex] \frac{2m^2-4m}{2(m-2)} = \frac{2m(m-2)}{2(m-2)} =m[/tex]
[tex] \frac{m^2-2m+1}{m-1} = \frac{(m-1)^2}{m-1} =m-1[/tex]
[tex] \frac{m^2-3m+2}{m^2-m} = \frac{(m-2)(m-1)}{m(m-1)} = \frac{m-2}{m} [/tex]
[tex] \frac{m^2-m-2}{m^2-1} = \frac{(m+1)(m-2)}{(m+1)(m-1)} = \frac{m-2}{m-1} [/tex]
We can conclude that you should your rational expressions as follows:
[tex]\frac{m-2}{m}----\ \textgreater \ \frac{m^2-3m+2}{m^2-m} [/tex]
[tex]m-1----\ \textgreater \ \frac{m^2-2m+1}{m-1}[/tex]
[tex]\frac{m-2}{m-1}----\ \textgreater \ \frac{m^2-m-2}{m^2-1}[/tex]
[tex]m----\ \textgreater \ \frac{2m^2-4m}{2(m-2)}[/tex]
