Cách làm:
$a)$
$\frac{3m-5}{m-1}+\frac{2m-5}{2-m}=1$
$<=>(3m-5).(2-m)+(2m-5).(m-1)=(m-1).(2-m)$
$<=>6m-3m^2-10+5m+2m^2-2m-5m+5=2m-m^2-2+m$
$<=>m=3$
Vậy $m=3$ thì $\frac{3m-5}{m-1}+\frac{2m-5}{2-m}=1$
$b)$
$\frac{9m-7}{3m-2}+\frac{5-4m}{2m-3}=1$
$<=>(9m-7).(2m-3)+(5-4m).(3m-2)=(3m-2).(2m-3)$
$<=>18m^2-27m-14m+21+15m-10-12m^2+8m=6m^2-9m-4m+6$
$<=>-5m=-5$
$<=>m=1$
Vậy $m=1$ thì $\frac{9m-7}{3m-2}+\frac{5-4m}{2m-3}=1$