Question:
$m-\frac{m-1}{2}=1-\frac{m-2}{3}$
Solution:
Given $m-\frac{m-1}{2}=1-\frac{m-2}{3}$
$\Rightarrow$ $\frac{2 m-(m-1)}{2}=\frac{3-(m-2)}{3}$
$\Rightarrow$ $3(2 m-m+1)=2(3-m+2)$ [by cross multiplication]
$\Rightarrow \quad 3(m+1)=2(5-m)$
$\Rightarrow \quad 3 m+3=10-2 m$
$\Rightarrow$ $3 m+2 m=10-3$ [transposing $-2 m$ to LHS and 3 to RHS]
$\Rightarrow$ $5 m=7$
$\Rightarrow$ $\frac{5 m}{5}=\frac{7}{5}$ [dividing both sides by 5 ]
$\therefore$ $m=\frac{7}{5}$
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