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\(=\left(\dfrac{32}{99}\cdot\dfrac{14}{9}-\dfrac{25}{99}\right)\cdot\dfrac{11}{43}\)
\(=\dfrac{1}{99}\cdot\left(32\cdot\dfrac{14}{9}-25\right)\cdot\dfrac{11}{43}\)
\(=\dfrac{1}{43\cdot9}\cdot\dfrac{223}{9}=\dfrac{223}{3483}\)
\(=\left(\dfrac{32}{99}-\dfrac{14}{9}-\dfrac{25}{99}\right)\cdot\dfrac{11}{38}\)
\(=\left(\dfrac{7}{99}-\dfrac{154}{99}\right)\cdot\dfrac{11}{38}\)
\(=\dfrac{-147}{99}\cdot\dfrac{11}{38}=\dfrac{-49}{114}\)
\(\left[0,\left(32\right).1,\left(5\right)-0,\left(25\right)\right].\dfrac{11}{83}\)
\(=\left[\dfrac{32}{99}.\left(1+\dfrac{5}{9}\right)-\dfrac{25}{99}\right].\dfrac{11}{83}\)
\(=\left[\dfrac{32}{99}.\dfrac{14}{9}-\dfrac{25}{99}\right].\dfrac{11}{83}\)
\(=\left[\dfrac{448}{891}-\dfrac{25}{99}\right].\dfrac{11}{83}\)
\(=\dfrac{223}{891}.\dfrac{11}{83}\)
\(=\dfrac{223}{6723}\)
\(H=\left[0,\left(32\right).1,\left(5\right)-0,\left(25\right)\right].\dfrac{11}{83}\)
\(\Leftrightarrow H=\left(\dfrac{32}{99}.\dfrac{14}{9}-\dfrac{25}{99}\right).\dfrac{11}{83}\)
\(\Leftrightarrow H=\left(\dfrac{448}{891}-\dfrac{25}{99}\right).\dfrac{11}{83}\)
\(\Leftrightarrow H=\left(\dfrac{448}{891}-\dfrac{225}{891}\right).\dfrac{11}{83}\)
\(\Leftrightarrow H=\dfrac{448-225}{891}.\dfrac{11}{83}\)
\(\Leftrightarrow H=\dfrac{223}{891}.\dfrac{11}{83}\)
\(\Leftrightarrow H=\dfrac{2453}{73953}\)
\(\Leftrightarrow H=\dfrac{223}{6723}\)
2) \(A=\dfrac{0,5+0,\left(3\right)-0,1\left(6\right)}{2,5+1,\left(6\right)-0,8\left(3\right)}\)
\(\Leftrightarrow A=\dfrac{\dfrac{3}{6}+\dfrac{2}{6}-\dfrac{1}{6}}{\dfrac{15}{6}+\dfrac{10}{6}-\dfrac{5}{6}}\)
\(\Leftrightarrow A=\dfrac{\dfrac{3+2-1}{6}}{\dfrac{15+10-5}{6}}\)
\(\Leftrightarrow A=\dfrac{\dfrac{4}{6}}{\dfrac{20}{6}}\)
\(\Leftrightarrow A=\dfrac{4}{6}.\dfrac{6}{20}\)
\(\Leftrightarrow A=\dfrac{24}{120}\)
\(\Leftrightarrow A=\dfrac{1}{5}\)
