Question
Solve: $\text{m}-\frac{(\text{m}-1)}{2}=1-\frac{(\text{m}-2)}{3} $
✓
Answer
$\text{m}-\frac{(\text{m}-1)}{2}=1-\frac{(\text{m}-2)}{3} $
$\Rightarrow \frac{2\text{m} - \text{m} + 1}{2} = 1 −\frac{ ( \text{m}−2 )}{3}(L.C.M.$ of $1$ and $2$ is $2 )$
$\Rightarrow\frac{\text{m} + 1}{2} = \frac{3 −\text{m} + 2}{3} (L.C.M.$ of $1$ and $3$ is $3 )$
$\Rightarrow\frac{\text{m} + 1}{2} = \frac{5 −\text{ m}}{3}$
$\Rightarrow 3 ( \text{m} + 1 ) = 2 ( 5 - \text{m} ) ($by cross multiplication$)$
$\Rightarrow3\text{m} + 3 = 10 - 2\text{m}$
$3\text{m} + 2\text{m} = 10 - 3$
$\Rightarrow 5\text{m} = 7$
$\Rightarrow\text{m}= 75$
$\therefore \text{m} = \frac{7}{5}$
$\Rightarrow \frac{2\text{m} - \text{m} + 1}{2} = 1 −\frac{ ( \text{m}−2 )}{3}(L.C.M.$ of $1$ and $2$ is $2 )$
$\Rightarrow\frac{\text{m} + 1}{2} = \frac{3 −\text{m} + 2}{3} (L.C.M.$ of $1$ and $3$ is $3 )$
$\Rightarrow\frac{\text{m} + 1}{2} = \frac{5 −\text{ m}}{3}$
$\Rightarrow 3 ( \text{m} + 1 ) = 2 ( 5 - \text{m} ) ($by cross multiplication$)$
$\Rightarrow3\text{m} + 3 = 10 - 2\text{m}$
$3\text{m} + 2\text{m} = 10 - 3$
$\Rightarrow 5\text{m} = 7$
$\Rightarrow\text{m}= 75$
$\therefore \text{m} = \frac{7}{5}$
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