Aritmetica

1/5+6/37*((7/6/(2/3+6/5)*14/45+3/4)+1/12) -1/6

1/5+6/37*((7/6 *(15/28*14/45)+3/4)+1/12)-1/6

1/5+6/37*(7/6*1/6+3/4)+1/12)-1/6

1/5+6/37*37/36-1/6

1/5+1/6-1/6 = 1/5 

$\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\left(\dfrac{2}{3}+\dfrac{1}{2}\right) : \left(\dfrac{2}{3}+\dfrac{4}{9}·\dfrac{27}{10}\right)·\dfrac{14}{45}+\dfrac{3}{2^2}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\left(\dfrac{4+3}{6}\right) : \left(\dfrac{2}{3}+\dfrac{\cancel4^2}{\cancel9_1}·\dfrac{\cancel{27}^3}{\cancel{10}_5}\right)·\dfrac{14}{45}+\dfrac{3}{4}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\dfrac{7}{6} : \left(\dfrac{2}{3}+\dfrac{2}{1}·\dfrac{3}{5}\right)·\dfrac{14}{45}+\dfrac{3}{4}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\dfrac{7}{6} : \left(\dfrac{2}{3}+\dfrac{6}{5}\right)·\dfrac{14}{45}+\dfrac{3}{4}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\dfrac{7}{6} : \left(\dfrac{10+18}{15}\right)·\dfrac{14}{45}+\dfrac{3}{4}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\dfrac{7}{6} : \dfrac{28}{15}·\dfrac{14}{45}+\dfrac{3}{4}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\dfrac{7}{6}·\dfrac{15}{28}·\dfrac{14}{45}+\dfrac{3}{4}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\dfrac{7}{6}·\dfrac{\cancel{15}^1}{\cancel{28}_2}·\dfrac{\cancel{14}^1}{\cancel{45}_3}+\dfrac{3}{4}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\dfrac{7}{6}·\dfrac{1}{2}·\dfrac{1}{3}+\dfrac{3}{4}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\dfrac{7}{36}+\dfrac{3}{4}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\left[\dfrac{7+27}{36}\right]+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\dfrac{34}{36}+\dfrac{1}{12}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\left\{\dfrac{34+3}{36}\right\}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{6}{37}·\dfrac{37}{36}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{\cancel6^1}{\cancel{37}_1}·\dfrac{\cancel{37}^1}{\cancel{36}_6}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{1}{1}·\dfrac{1}{6}-\dfrac{1}{6}=$

$=\dfrac{1}{5}+\dfrac{1}{6}-\dfrac{1}{6}=$

$=\dfrac{1}{5}$