Question

equaçao 
$\frac{2x-1}{3} - \frac{5x-10}{4}= \frac{3x-1}{5} - \frac{9(x-2)}{6}$

Answer 1

$\dfrac{2x - 1}{3} - \dfrac{5x - 10}{4} = \dfrac{3x - 1}{5} - \dfrac{9(x - 2)}{6}$

Resolvendo por partes
1º parte

MMC de 3, 4 = 12

2º parte 

MMC DE 5, 6 = 30

$\dfrac{2x - 1}{3} - \dfrac{5x - 10}{4} = \dfrac{3x - 1}{5} - \dfrac{9x - 18)}{6} \\ \\ \\ \dfrac{4x - 4 - 15x - 30 }{12} = \dfrac{18x - 6 - 45x + 90}{30} \\ \\ \\ -\dfrac{7x - 26}{12} = -\dfrac{27x - 96}{30}$

Simplificando o segundo termo , dividir por 3

$-\dfrac{7x - 26}{12} = -\dfrac{9x - 28}{10}$

$-\dfrac{7x - 26}{12} + \dfrac{9x - 28}{10} = 0$

MMC DE 12, 10 = 60

$\dfrac{-35X + 130 + 54X - 168}{60} =0 \\ \\ \\ \dfrac{19x - 38}{60} =0 \\ \\ \\ 19x - 38 = 0 \\ \\ 19x = 38 \\ \\ \\ x = \dfrac{38}{19} \\ \\ \\ => x = 2$