Espressione numero 233

Riduci il più possibile i termini; quindi applichi la proprietà delle proporzioni "il prodotto dei medi è uguale a quello degli estremi" (4° rigo)

(5/6 + 4/15 - 9/8·(2/3))/(3/2 - 6/5 + 13/15) = (4/5·(5/6) - 11/30)/x

(5/6 + 4/15 - 3/4)/(3/2 - 6/5 + 13/15) = (2/3 - 11/30)/x

7/20/(7/6) = 3/10/x

proprietà fondamentale proporzioni:

7/20·x = 7/6·(3/10)

7/20·x = 7/20

x = 1

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$\small \left(\dfrac{5}{6}+\dfrac{4}{15}-\dfrac{\cancel9^3}{\cancel8_4}·\dfrac{\cancel2^1}{\cancel3_1}\right) : \left(\dfrac{3}{2}-\dfrac{6}{5}+\dfrac{13}{15}\right) = \left(\dfrac{\cancel4^2}{\cancel5_1}·\dfrac{\cancel5^1}{\cancel6_3}-\dfrac{11}{30}\right) : x $

$\small \left(\dfrac{5}{6}+\dfrac{4}{15}-\dfrac{3}{4}\right) : \left(\dfrac{45-36+26}{30}\right) = \left(\dfrac{2}{1}·\dfrac{1}{3}-\dfrac{11}{30}\right) : x $

$\small \left(\dfrac{50+16-45}{60}\right) : \dfrac{\cancel{35}^7}{\cancel{30}_6} = \left(\dfrac{2}{3}-\dfrac{11}{30}\right) : x $

$\small \dfrac{\cancel{21}^7}{\cancel{60}_{20}} : \dfrac{7}{6} = \left(\dfrac{20-11}{30}\right) : x $

$\small \dfrac{7}{20} : \dfrac{7}{6} = \dfrac{\cancel9^3}{\cancel{30}_{10}} : x $

$\small \dfrac{7}{20} : \dfrac{7}{6} = \dfrac{3}{10} : x $

$\small x=\dfrac{1}{2} ·2$

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

$\small x=1 $