Question

5/m-1 - 3/m-2= 2/m-3​

Answer 1

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

$= > \frac{5(m - 2) - 3(m - 1) }{(m - 1)(m - 2)} = \frac{2}{m - 3}$

$= > \frac{(5m - 10) - (3m - 6)}{ {m}^{2} + {( - 1 + ( - 2))}m - ( - 1 \times - 2) } = \frac{2}{m - 3)}$

$= > \frac{5m - 10 - 3m + 6}{ {m}^{2} + ( - 1 - 2)m - (2) } = \frac{2}{m - 3}$

$= > \frac{5m - 3m - 10 + 6}{ {m}^{2} + ( - 3m) - 2 } = \frac{2}{m - 3}$

$= > \frac{2m - 4}{ {m}^{2} - 3m - 2 } = \frac{2}{m - 3}$

$= > (2m - 4)(m - 3) = 2( {m}^{2} - 3m - 2)$

$= > {2m}^{2} - 6m - 4m + 12 = {2m}^{2} - 6m - 4$

$= > {2m}^{2} - {2m}^{2} - 6m + 6m - 4m + 12 + 4 = 0$

$= > 4m + 16 = 0$

$= > m = - \frac{16}{4}$

$= > m = ( - 4)$