Frazioni

1 + 5/3·2^2·(6/5 - 1)^6/(1 - 4/5)^4 + (21/25 + 14/75)·(25/11)=

=1 + 5/3·4·(1/5)^6/(1/5)^4 + 77/75·(25/11)=

=1 + 5/3·4·(1/5)^2 + 7/3=

=1 + 4/15 + 7/3=

=(15 + 4 + 7·5)/15 = 18/5

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$\small 1+\dfrac{5}{3}·2^2·\left(\dfrac{6}{5}-1\right)^6 : \left(1-\dfrac{4}{5}\right)^4+\left(\dfrac{21}{25}+\dfrac{14}{75}\right)·\dfrac{25}{11}=$

$\small =1+\dfrac{5}{3}·4·\left(\dfrac{6-5}{5}\right)^6 : \left(\dfrac{5-4}{5}\right)^4+\left(\dfrac{63+14}{75}\right)·\dfrac{25}{11}=$

$\small =1+\dfrac{20}{3}·\left(\dfrac{1}{5}\right)^6 : \left(\dfrac{1}{5}\right)^4+\dfrac{\cancel{77}^7}{\cancel{75}_3}·\dfrac{\cancel{25}^1}{\cancel{11}_1}=$

$\small =1+\dfrac{20}{3}·\left(\dfrac{1}{5}\right)^{6-4} +\dfrac{7}{3}·\dfrac{1}{1}=$

$\small =1+\dfrac{20}{3}·\left(\dfrac{1}{5}\right)^2 +\dfrac{7}{3}=$

$\small =1+\dfrac{\cancel{20}^4}{3}·\dfrac{1}{\cancel{25}_5} +\dfrac{7}{3}=$

$\small =1+\dfrac{4}{3}·\dfrac{1}{5} +\dfrac{7}{3}=$

$\small =1+\dfrac{4}{15} +\dfrac{7}{3}=$

$\small =\dfrac{15+4+35}{15} =$

$\small =\dfrac{\cancel{54}^{18}}{\cancel{15}_5} =$

$\small = \dfrac{18}{5}$