[Risolto] Algebra

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$\left({5\over3}-{3\over11}\right) ÷ \left[-{8\over3}+{6\over7}·\left(-{7\over6}\right)^2-{12\over11}-\left({5\over8}-1+{5\over4}\right) ÷ \left(-2+{1\over4}\right)\right]=$

$=\left({55-9\over33}\right) ÷ \left[-{8\over3}+{\cancel6^1\over\cancel7_1}·{\cancel{49}^7\over\cancel{36}_6}-{12\over11}-\left({5-8+10\over8}\right) ÷ \left({-8+1\over4}\right)\right]=$

$={46\over33} ÷ \left[-{8\over3}+{1\over1}·{7\over6}-{12\over11}-{7\over8} ÷ \left(-{7\over4}\right)\right]=$

$={46\over33} ÷ \left[-{8\over3}+{7\over6}-{12\over11}-{7\over8}·\left(-{4\over7}\right)\right]=$

$={46\over33} ÷ \left[-{8\over3}+{7\over6}-{12\over11}-{\cancel7^1\over\cancel8_2}·\left(-{\cancel4^1\over\cancel7_1}\right)\right]=$

$={46\over33} ÷ \left[-{8\over3}+{7\over6}-{12\over11}-{1\over2}·\left(-{1\over1}\right)\right]=$

$={46\over33} ÷ \left[-{8\over3}+{7\over6}-{12\over11}+{1\over2}\right]=$

$={46\over33} ÷ \left[{-176+77-72+33\over66}\right]=$

$={46\over33} ÷ \left[-{\cancel{138}^{23}\over\cancel{66}_{11}}\right]=$

$={46\over33} ÷ \left[-{23\over11}\right]=$

$={\cancel{46}^2\over\cancel{33}_3}·\left[-{\cancel{11}^1\over\cancel{23}_1}\right]=$

$={2\over3}·\left[-{1\over1}\right]=$

$=-{2\over3}$