Question

como faço a resolução da seguinte equação?
$\frac{m}{6} + \frac{m}{9} = \frac{1}{15} + \frac{m - \frac{1}{2} }{3}$

Answer 1

$\rightarrow\frac{m}{6}+\frac{m}{9}= \frac{1}{15}+ \frac{m- \frac{1}{2} }{3}$

MMC 6,9,15,3=90

$90\cdot\frac{m}{6}+90\cdot\frac{m}{9}= 90\cdot\frac{1}{15}+ 90\cdot\frac{m- \frac{1}{2} }{3}$

$90\cdot\frac{m}{\not6}+90\cdot\frac{m}{\not9}= 90\cdot\frac{1}{\not15}+ 90\cdot\frac{m- \frac{1}{2} }{\not3}$

$15m+10m=6+30\cdot (m- \frac{1}{2} )$

$15m+10m=6+15\left(2m-1\right)$

$25m=6+15\left(2m-1\right)$

$25m=30m-9$

$-5m=-9$

$m= \frac{-9}{-5}= \frac{9}{5}$

Answer 2

Vamos ao caso:

$\frac{m}{6} + \frac{m}{9} = \frac{1}{15} + \frac{2m - 1}{6}$

$\frac{15m + 10m = 6 + 15*(2m - 1)}{90}$

15m + 10m = 6 + 30m -15

30m - 25m = 15 - 6

5m = 9

m = $\frac{9}{5}$