Espressioni

Si svolge come segue

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$\small \left(0,5+0,\overline3\right)^2 : \left(1,\overline6\right)^2+\left[\left(\dfrac{7}{10} : 0,9\overline3+2,\overline6 : 0,\overline4\right)·\dfrac{2}{27}+\dfrac{5}{12}\right]=$

$\small =\left(\dfrac{5}{10}+\dfrac{3-0}{9}\right)^2 : \left(\dfrac{16-1}{9}\right)^2+\left[\left(\dfrac{7}{10} : \dfrac{93-9}{90}+\dfrac{26-2}{9} : \dfrac{4-0}{9}\right)·\dfrac{2}{27}+\dfrac{5}{12}\right]=$

$\small =\left(\dfrac{\cancel5^1}{\cancel{10}_2}+\dfrac{\cancel3^1}{\cancel9_3}\right)^2 : \left(\dfrac{\cancel{15}^5}{\cancel9_3}\right)^2+\left[\left(\dfrac{7}{10} : \dfrac{\cancel{84}^{14}}{\cancel{90}_{15}}+\dfrac{\cancel{24}^8}{\cancel9_3} : \dfrac{4}{9}\right)·\dfrac{2}{27}+\dfrac{5}{12}\right]=$

$\small =\left(\dfrac{1}{2}+\dfrac{1}{3}\right)^2 : \left(\dfrac{5}{3}\right)^2+\left[\left(\dfrac{7}{10} : \dfrac{14}{15}+\dfrac{\cancel8^2}{\cancel3_1}·\dfrac{\cancel9^3}{\cancel4_1}\right)·\dfrac{2}{27}+\dfrac{5}{12}\right]=$

$\small =\left(\dfrac{3+2}{6}\right)^2 : \dfrac{25}{9}+\left[\left(\dfrac{\cancel7^1}{\cancel{10}_2}·\dfrac{\cancel{15}^3}{\cancel{14}_2}+\dfrac{2}{1}·\dfrac{3}{1}\right)·\dfrac{2}{27}+\dfrac{5}{12}\right]=$

$\small =\left(\dfrac{5}{6}\right)^2·\dfrac{9}{25}+\left[\left(\dfrac{1}{2}·\dfrac{3}{2}+6\right)·\dfrac{2}{27}+\dfrac{5}{12}\right]=$

$\small = \dfrac{\cancel{25}^1}{\cancel{36}_4}·\dfrac{\cancel9^1}{\cancel{25}_1}+\left[\left(\dfrac{3+24}{4}\right)·\dfrac{2}{27}+\dfrac{5}{12}\right]=$

$\small = \dfrac{1}{4}·\dfrac{1}{1}+\left[\dfrac{\cancel{27}^1}{\cancel4_2}·\dfrac{\cancel2^1}{\cancel{27}_1}+\dfrac{5}{12}\right]=$

$\small = \dfrac{1}{4}+\left[\dfrac{1}{2}·\dfrac{1}{1}+\dfrac{5}{12}\right]=$

$\small = \dfrac{1}{4}+\left[\dfrac{1}{2}+\dfrac{5}{12}\right]=$

$\small = \dfrac{1}{4}+\left[\dfrac{6+5}{12}\right]=$

$\small = \dfrac{1}{4}+\dfrac{11}{12}=$

$\small = \dfrac{3+11}{12}=$

$\small = \dfrac{\cancel{14}^7}{\cancel{12}_6}= \dfrac{7}{6}$