[Risolto] ESPRESSIONE DI MATEMATICA

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$\small{(-0,8\overline3)^2-\frac{3}{2}·\big[-1,\overline3·\big(-\frac{1}{2}\big)^2-1\big]^2-\big(-\frac{1}{2}+\frac{1}{3}\big)^2-\big[-\big(-\frac{1}{3}\big)^2+(-0,5)^3\big]-\big(\frac{3}{2}\big)^3-7·\big(\frac{1}{6}\big)^2}$ =

= $(-\frac{83-8}{90})^2-\frac{3}{2}·\big[-\frac{13-1}{9}·\frac{1}{4}-1\big]^2-\big(\frac{-3+2}{6}\big)^2-\big[-\frac{1}{9}+\big(-\frac{1}{2}\big)^3\big]-\frac{27}{8}-\frac{7}{36}$ =

= $(-\frac{75}{90})^2-\frac{3}{2}·\big[-\frac{12}{9}·\frac{1}{4}-1\big]^2-\big(\frac{-1}{6}\big)^2-\big[-\frac{1}{9}-\frac{1}{8}\big]-\frac{27}{8}-\frac{7}{36}$ =

= $(-\frac{5}{6})^2-\frac{3}{2}·\big[-\frac{4}{3}·\frac{1}{4}-1\big]^2-\frac{1}{36}-\big[\frac{-8-9}{72}\big]-\frac{27}{8}-\frac{7}{36}$ =

= $\frac{25}{36}-\frac{3}{2}·\big[-\frac{1}{3}·\frac{1}{1}-1\big]^2-\frac{1}{36}-\big[-\frac{17}{72}\big]-\frac{27}{8}-\frac{7}{36}$ =

= $\frac{25}{36}-\frac{3}{2}·\big[-\frac{1}{3}-1\big]^2-\frac{1}{36}+\frac{17}{72}-\frac{27}{8}-\frac{7}{36}$ =

= $\frac{25}{36}-\frac{3}{2}·\big[\frac{-1-3}{3}\big]^2+\big(\frac{-4+34-486-28}{144}\big)$ =

= $\frac{25}{36}-\frac{3}{2}·\big[-\frac{4}{3}\big]^2+(\frac{-484}{144}\big)$ =

= $\frac{25}{36}-\frac{3}{2}·\frac{16}{9}-\frac{121}{36}$ =

= $\frac{25}{36}-\frac{1}{1}·\frac{8}{3}-\frac{121}{36}$ =

= $\frac{25}{36}-\frac{8}{3}-\frac{121}{36}$ =

= $\frac{25-96-121}{36}$ =

= $-\frac{192}{36}$ =

= $-\frac{16}{3}$ $(= -5,\overline3)$.