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Moltiplicazioni:

1)  1/2 x 1/3 = (1 x 1) / (2 x 3) =  1/6;

2) dentro la seconda parentesi tonda:

10/9 x 3/2 = (10 x 3) / (9 x 2)  = (5 x 1) / (3 x 1) =  5/3; il 10 si semplifica con 2, rimane 5;

il 3 si semplifica con 9;  rimane 5/3.

mcm(7; 14) = 14;  mcm(3; 4) = 12.

[1/2 x 1/3 + (2/14 + 12/14) + (10/9 x 3/2 - 3/4)] - 1/10 x 5/1 - 7/12 =

[1/6 + (2/14 + 12/14) + (5/3 - 3/4)] - 1/10 x 5/1 - 7/12 =

=  [1/6 + 14/14 + (20/12 - 9/12)] - 1/2 - 7/12 =

= [1/6 + 1 + 11/12] - 1/2  - 7/12 =

mcm(6; 1; 12) = 12.

= [2/12 + 12/12 + 11/12] - 1/2 - 7/12 =

=  25/12 - 1/2 - 7/12 =

= 25/12 - 6/12 - 7/12 =

= 12/12 = 1.

Ciao @andreag

$\small \left[\dfrac{1}{2}·\dfrac{1}{3}+\left(\dfrac{1}{7}+\dfrac{\cancel{12}^6}{\cancel{14}_7}\right)+\left(\dfrac{\cancel{10}^5}{\cancel9_3}·\dfrac{\cancel3^1}{\cancel2_1}-\dfrac{3}{4}\right)\right]-\dfrac{1}{10} : \dfrac{1}{5}-\dfrac{7}{12}=$

$\small =\left[\dfrac{1}{6}+\left(\dfrac{1}{7}+\dfrac{6}{7}\right)+\left(\dfrac{5}{3}·\dfrac{1}{1}-\dfrac{3}{4}\right)\right]-\dfrac{1}{10}·\dfrac{5}{1}-\dfrac{7}{12}=$

$\small =\left[\dfrac{1}{6}+\dfrac{7}{7}+\left(\dfrac{5}{3}-\dfrac{3}{4}\right)\right]-\dfrac{1}{\cancel{10}_2}·\dfrac{\cancel5^1}{1}-\dfrac{7}{12}=$

$\small =\left[\dfrac{1}{6}+1+\left(\dfrac{20-9}{12}\right)\right]-\dfrac{1}{2}·\dfrac{1}{1}-\dfrac{7}{12}=$

$\small =\left[\dfrac{1}{6}+1+\dfrac{11}{12}\right]-\dfrac{1}{2}-\dfrac{7}{12}=$

$\small =\left[\dfrac{2+12+11}{12}\right]-\dfrac{1}{2}-\dfrac{7}{12}=$

$\small =\dfrac{25}{12}-\dfrac{1}{2}-\dfrac{7}{12}=$

$\small =\dfrac{25-6-7}{12}=$

$\small =\dfrac{12}{12}= 1$