[Risolto] espressione help

159)

$\frac{9}{4}·0,\overline6 + \big\{2,1\overline6 -\big[\frac{2}{5}+\big(1,1\overline6 -\frac{1}{4}+2\big)\big]·\big[\big(\frac{5}{4}-1,1\overline6 +1,\overline6 \big)-\frac{9}{8}\big]\big\}·3,\overline5$ =

= $\frac{9}{4}·\frac{6}{9} + \big\{\frac{216-21}{90} -\big[\frac{2}{5}+\big(\frac{116-11}{90} -\frac{1}{4}+2\big)\big]·\big[\big(\frac{5}{4}-\frac{116-11}{90} +\frac{16-1}{9} \big)-\frac{9}{8}\big]\big\}·\frac{35-3}{9}$ =

= $\frac{9}{4}·\frac{2}{3} + \big\{\frac{195}{90} -\big[\frac{2}{5}+\big(\frac{105}{90} -\frac{1}{4}+2\big)\big]·\big[\big(\frac{5}{4}-\frac{105}{90} +\frac{15}{9} \big)-\frac{9}{8}\big]\big\}·\frac{32}{9}$ =

= $\frac{3}{2}·\frac{1}{1} + \big\{\frac{13}{6} -\big[\frac{2}{5}+\big(\frac{7}{6} -\frac{1}{4}+2\big)\big]·\big[\big(\frac{5}{4}-\frac{7}{6} +\frac{5}{3} \big)-\frac{9}{8}\big]\big\}·\frac{32}{9}$ =

= $\frac{3}{2}+\big\{\frac{13}{6} -\big[\frac{2}{5}+\big(\frac{14-3+24}{12}\big)\big]·\big[\big(\frac{15-14+20}{12}\big)-\frac{9}{8}\big]\big\}·\frac{32}{9}$ =

= $\frac{3}{2}+\big\{\frac{13}{6} -\big[\frac{2}{5}+\frac{35}{12}\big]·\big[\frac{21}{12}-\frac{9}{8}\big]\big\}·\frac{32}{9}$ =

= $\frac{3}{2}+\big\{\frac{13}{6} -\big[\frac{24+175}{60}\big]·\big[\frac{7}{4}-\frac{9}{8}\big]\big\}·\frac{32}{9}$ =

= $\frac{3}{2}+\big\{\frac{13}{6} -\frac{199}{60}·\big[\frac{14-9}{8}\big]\big\}·\frac{32}{9}$ =

= $\frac{3}{2}+\big\{\frac{13}{6} -\frac{199}{60}·\frac{5}{8}\big\}·\frac{32}{9}$ =

= $\frac{3}{2}+\big\{\frac{13}{6} -\frac{199}{12}·\frac{1}{8}\big\}·\frac{32}{9}$ =

= $\frac{3}{2}+\big\{\frac{13}{6} -\frac{199}{96}\big\}·\frac{32}{9}$ =

= $\frac{3}{2}+\big\{\frac{208-199}{96}\big\}·\frac{32}{9}$ =

= $\frac{3}{2}+\frac{9}{96}·\frac{32}{9}$ =

= $\frac{3}{2}+\frac{3}{32}·\frac{32}{9}$ =

= $\frac{3}{2}+\frac{1}{1}·\frac{1}{3}$ =

= $\frac{3}{2}+\frac{1}{3}$ =

= $\frac{9+2}{6}$ =

= $\frac{11}{6}$ =