Question

Resolva a expressao simplificando quando possivel.

Answer 1

1/2 - [4/3 -14/45] ⁻² =
        [      23/15 ]
 

1/2 - [ 46/15 - 15/23] ⁻²=

1/2 - [2/3]⁻² =

1/2 - 9/4 =
- 7/4

Answer 2

Primeiramente iremos determinar a fração geratriz:

๏ $1,\overline{3}=1,333...=\frac{13-1}{9}=\frac{4}{3}$
๏ $0,3\overline{1}=0,3111...=\frac{31-3}{90}=\frac{14}{45}$

Logo:

$\frac{1}{2}-\left(\frac{\frac{4}{3}-\frac{14}{45}}{\frac{23}{15}}\right)^{-2}\\\frac{1}{2}-\left(\frac{\frac{46}{45}}{\frac{23}{15}}\right)^{-2}\\\frac{1}{2}-\left(\frac{46}{45}\cdot \frac{15}{23}\right)^{-2}\\\frac{1}{2}-\left(\frac{2}{3}\cdot \frac{1}{1}\right)^{-2}\\\frac{1}{2}-\left(\frac{2}{3}\right)^{-2}\\\frac{1}{2}-\left(\frac{3}{2}\right)^2\\\frac{1}{2}-\frac{9}{4}\\\boxed{\bold{-\frac{7}{4}}}$