Question

o valor da expressão (1/6-1/3)/(1/6+1/2)2+3/2

Answer 1

$(\frac{1}{6}- \frac{1}{3}/ (\frac{1}{6} + \frac{1}{2})^2+ \frac{3}{2}$

$\frac{-1}{6}/ (\frac{2}{3})^2+ \frac{3}{2}= \frac{-1}{6} / \frac{4}{9} + \frac{3}{2}= \frac{-1}{6}/ \frac{35}{18}$

$\frac{-1}{6}* \frac{18}{35}= \frac{-3}{35}$

Answer 2

$(\dfrac{ \dfrac{1}{6} - \dfrac{1}{3}}{ \dfrac{1}{6} + \dfrac{1}{2}}) ^2 + \dfrac{3}{2} \\ \\ \\ (\dfrac{ \dfrac{-1}{6}}{ \dfrac{2}{3}}) ^2 + \dfrac{3}{2}$

A fração que esta dividindo passa multiplicando e invertida:

$( \dfrac{-1}{6}} * \dfrac{3}{2}) ^2 + \dfrac{3}{2} \\ \\ \\ (\dfrac{- 1 * 3}{6 * 2})^2 + \dfrac{3}{2} \\ \\ \\ (\dfrac{- 3}{12})^2 + \dfrac{3}{2} \\ \\ \\ (\dfrac{- 1}{4})^2 + \dfrac{3}{2}$

$\dfrac{- 1}{16} + \dfrac{3}{2} \\ \\ \\ \\ => \dfrac{25}{16}$