Solve the following

$m-\frac{(m-1)}{2}=1-\frac{(m-2)}{3}$

$\Rightarrow \frac{2 m-m+1}{2}=1-\frac{(m-2)}{3} \quad($ L.C.M. of 1 and 2 is 2$)$

$\Rightarrow \frac{m+1}{2}=\frac{3-m+2}{3}$     ($ L.C.M. of 1 and 3 is 3$)$

$\Rightarrow \frac{m+1}{2}=\frac{5-m}{3}$

$\Rightarrow 3(m+1)=2(5-m) \quad \quad$ (by cross multiplication)

$\Rightarrow 3 m+3=10-2 m$

$\Rightarrow 3 m+2 m=10-3$

$\Rightarrow 5 m=7$

$\Rightarrow m=\frac{7}{5}$

$\therefore m=\frac{7}{5}$