Espressione

(3/8+(7/4*3/14*8/9+2/3))-(3/10+1/15-1/6)

(3/8+(3/8*8/9+2/3)-(9+2-5)/30

3/8+1/2+2/3-1/5

3/8+1-1/5

11/8-1/5

(55-8)/40 

47/40 

1,17500...

174)

$\small \left[0,375+\left(1,75 : 4,\overline6·0,\overline8+0,\overline6\right)\right]-\left(0,3+0,0\overline6-0,1\overline6\right)=$

$\small =\left[\dfrac{\cancel{375}^3}{\cancel{1000}_8}+\left(\dfrac{\cancel{175}^7}{\cancel{100}_4} : \dfrac{46-4}{9}·\dfrac{8-0}{9}+\dfrac{6-0}{9}\right)\right]-\left(\dfrac{3}{10}+\dfrac{6-0}{90}-\dfrac{16-1}{90}\right)=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{7}{4} : \dfrac{\cancel{42}^{14}}{\cancel9_3}·\dfrac{8}{9}+\dfrac{\cancel6^2}{\cancel9_3}\right)\right]-\left(\dfrac{3}{10}+\dfrac{\cancel6^1}{\cancel{90}_{15}}-\dfrac{\cancel{15}^1}{\cancel{90}_6}\right)=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{7}{4} : \dfrac{14}{3}·\dfrac{8}{9}+\dfrac{2}{3}\right)\right]-\left(\dfrac{3}{10}+\dfrac{1}{15}-\dfrac{1}{6}\right)=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{\cancel7^1}{\cancel4_1}·\dfrac{\cancel3^1}{\cancel{14}_2}·\dfrac{\cancel8^2}{\cancel9_3}+\dfrac{2}{3}\right)\right]-\left(\dfrac{9+2-5}{30}\right)=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{1}{1}·\dfrac{1}{2}·\dfrac{2}{3}+\dfrac{2}{3}\right)\right]-\dfrac{\cancel6^1}{\cancel{30}_5}=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{\cancel2^1}{\cancel6_3}+\dfrac{2}{3}\right)\right]-\dfrac{1}{5}=$

$\small =\left[\dfrac{3}{8}+\left(\dfrac{1}{3}+\dfrac{2}{3}\right)\right]-\dfrac{1}{5}=$

$\small =\left[\dfrac{3}{8}+\dfrac{\cancel3^1}{\cancel3_1}\right]-\dfrac{1}{5}=$

$\small =\left[\dfrac{3}{8}+1\right]-\dfrac{1}{5}=$

$\small =\left[\dfrac{3+8}{8}\right]-\dfrac{1}{5}=$

$\small = \dfrac{11}{8}-\dfrac{1}{5}=$

$\small = \dfrac{55-8}{40}= \dfrac{47}{40}$

$\small (= 1,175).$