Question

$\frac{m-3}{m+2} -\frac{m-2}{m²-4} = \frac{m}{m-2}$

Answer 1

Vamos lá :

$\dfrac{m-3}{m+2} - \dfrac{m-2}{m^{2} - 4} = \dfrac{m}{m-2} \\\\  \\ \\ \dfrac{m-3}{m+2} - \dfrac{m-2}{(m + 2)(m - 2)} = \dfrac{m}{m-2}\\ \\ \\ \\ MMC =  (m + 2)(m - 2)\\ \\ \\ \\ \dfrac{(m - 3)(m - 2)}{(m + 2)(m - 2)} - \dfrac{(m - 2)}{(m + 2)(m - 2)} = \dfrac{m(m + 2)}{(m + 2)(m - 2)} \\ \\ \\ (m - 3)(m - 2) - (m - 2)= m(m + 2)\\ \\ \\ m^{2}-2m -3m+ 6- m + 2 = m^{2} + 2m\\ \\ \\ m^{2} - 6m +8 = m^{2} + 2m\\ \\ \\ m^{2 }-m^{2} - 6m - 2m + 8 = 0\\ \\ \\ -8m + 8 = 0\\ \\ \\ m = \dfrac{- 8}{- 8}$

$\boxed{\boxed{m = +~ 1}}$

Espero ter ajudado !!!