Aritmetica

$\small \left\{\left[\left(\dfrac{3}{4}+\dfrac{1}{8}\right)^2·\left(\dfrac{4}{7}\right)^2+\dfrac27\right] : \left(\dfrac{3}{7}\right)^2-\left[\left(\dfrac12-\dfrac37\right)^2·\dfrac{14}3\right]\right\}: \dfrac{3^2}{14}=$

$ =\small \left\{\left[\left(\dfrac{6+1}{8}\right)^2·\dfrac{16}{49}+\dfrac27\right] : \dfrac9{49}-\left[\left(\dfrac{7-6}{14}\right)^2·\dfrac{14}{3}\right]\right\}: \dfrac{9}{14}=$

$ =\small \left\{\left[\left(\dfrac{7}{8}\right)^2·\dfrac{16}{49}+\dfrac{2}{7}\right]·\dfrac{49}{9}-\left[\left(\dfrac{1}{14}\right)^2·\dfrac{14}{3}\right]\right\}·\dfrac{14}{9}=$

$ =\small \left\{\left[\dfrac{\cancel{49}^1}{\cancel{64}_4}·\dfrac{\cancel{16}^1}{\cancel{49}_1}+\dfrac{2}{7}\right]·\dfrac{49}{9}-\left[\dfrac{1}{\cancel{196}_{14}}·\dfrac{\cancel{14}^1}{3}\right]\right\}·\dfrac{14}{9}=$

$ =\small \left\{\left[\dfrac{1}{4}+\dfrac{2}{7}\right]·\dfrac{49}{9}-\left[\dfrac{1}{14}·\dfrac{1}{3}\right]\right\}·\dfrac{14}{9}=$

$ =\small \left\{\left[\dfrac{7+8}{28}\right]·\dfrac{49}{9}-\dfrac{1}{42}\right\}·\dfrac{14}{9}=$

$ =\small \left\{\dfrac{\cancel{15}^5}{\cancel{28}_4}·\dfrac{\cancel{49}^7}{\cancel9_3}-\dfrac{1}{42}\right\}·\dfrac{14}{9}=$

$ =\small \left\{\dfrac{5}{4}·\dfrac{7}{3}-\dfrac{1}{42}\right\}·\dfrac{14}{9}=$

$ =\small \left\{\dfrac{35}{12}-\dfrac{1}{42}\right\}·\dfrac{14}{9}=$

$ =\small \left\{\dfrac{245-2}{84}\right\}·\dfrac{14}{9}=$

$ =\small \dfrac{\cancel{243}^{27}}{\cancel{84}_6}·\dfrac{\cancel{14}^1}{\cancel9_1}=$

$ =\small \dfrac{27}{6}·\dfrac{1}{1}=$

$= \small \dfrac{\cancel{27}^9}{\cancel6_2}=$

$= \small \dfrac{9}{2}$