SOLUTION
We want to match each expression to its simplest form, we have
(a)
[tex]\begin{gathered} \frac{2m^2-4m}{2(m-2)} \\ factorizing\text{ we have } \\ =\frac{2m(m-2)}{2(m-2)} \\ cancelling\text{ common terms we have } \\ =m \end{gathered}[/tex]hence the answer is m
(b)
[tex]\begin{gathered} \frac{m^2-2m+1}{m-1} \\ =\frac{m^2-m-m+1_}{m-1} \\ =\frac{m(m-1)-1(m-1)}{m-1} \\ =\frac{(m-1)(m-1)}{m-1} \\ cancelling\text{ m - 1, we have } \\ =m-1 \end{gathered}[/tex]hence the answer is m - 1
(c)
[tex]\begin{gathered} \frac{m^2-3m+2}{m^2-m} \\ =\frac{m^2-2m-m+2}{m^2-m} \\ factorizing\text{ we have } \\ \frac{m(m-2)-1(m-2)}{m(m-1)} \\ =\frac{(m-1)(m-2)}{m(m-1)} \\ canceling\text{ m - 1, we have } \\ =\frac{m-2}{m} \end{gathered}[/tex]Hence the answer is
[tex]\frac{m-2}{m}[/tex](d)
[tex]\begin{gathered} \frac{m^2-m-2}{m^2-1} \\ =\frac{m^2-2m+m-2}{m^2-1} \\ factorizing\text{ we have } \\ \frac{m(m-2)+1(m-2)}{(m-1)(m+1)} \\ =\frac{(m+1)(m-2)}{(m-1)(m+1)} \\ cancelling\text{ the common terms \lparen m + 1\rparen, we have } \\ =\frac{m-2}{m-1} \end{gathered}[/tex]Hence the answer is
[tex]\frac{m-2}{m-1}[/tex]