N° 936

Svolgimento a mano 

(2/3-x)÷x=[(2-1/2)^2x(2+1/2)-(3/4+1/2-1/6)]÷[(3+1/2)÷(3-1/3)+(3/4-1/2+1/6)]

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$\small \left(\dfrac{2}{3}-x\right) ÷ x = \left[\left(2-\dfrac{1}{2}\right)^2·\left(2+\dfrac{1}{2}\right)-\left(\dfrac{3}{4}+\dfrac{1}{2}-\dfrac{1}{6}\right)\right]÷\left[\left(3+\dfrac{1}{2}\right)÷\left(3-\dfrac{1}{3}\right)+\left(\dfrac{3}{4}-\dfrac{1}{2}+\dfrac{1}{6}\right)\right] $

$\small  \left(\dfrac{2}{3}-x\right) ÷ x = \left[\left(\dfrac{4-1}{2}\right)^2·\left(\dfrac{4+1}{2}\right)-\left(\dfrac{9+6-2}{12}\right)\right]÷\left[\left(\dfrac{6+1}{2}\right)÷\left(\dfrac{9-1}{3}\right)+\left(\dfrac{9-6+2}{12}\right)\right] $

$\small  \left(\dfrac{2}{3}-x\right) ÷ x = \left[\left(\dfrac{3}{2}\right)^2·\dfrac{5}{2}-\dfrac{13}{12}\right]÷\left[\dfrac{7}{2}÷\dfrac{8}{3}+\dfrac{5}{12}\right] $

$\small  \left(\dfrac{2}{3}-x\right) ÷ x = \left[\dfrac{9}{4}·\dfrac{5}{2}-\dfrac{13}{12}\right]÷\left[\dfrac{7}{2}·\dfrac{3}{8}+\dfrac{5}{12}\right] $

$\small  \left(\dfrac{2}{3}-x\right) ÷ x = \left[\dfrac{45}{8}-\dfrac{13}{12}\right]÷\left[\dfrac{21}{16}+\dfrac{5}{12}\right] $

$\small  \left(\dfrac{2}{3}-x\right) ÷ x = \left[\dfrac{135-26}{24}\right]÷\left[\dfrac{63+20}{48}\right] $

$\small  \left(\dfrac{2}{3}-x\right) ÷ x = \dfrac{109}{24}÷\dfrac{83}{48} $

$\small\text{avendo tutti i termini di una proporzione, applica il comporre per calcolare l'incognita come segue:}$ 

$\small  \left(\dfrac{2}{3}-x+x\right) ÷ x = \left(\dfrac{109}{24}+\dfrac{83}{48}\right)÷\dfrac{83}{48} $

$\small  \left(\dfrac{2}{3}\cancel{-x}\cancel{+x}\right) ÷ x = \left(\dfrac{218+83}{48}\right)÷\dfrac{83}{48} $

$\small  \dfrac{2}{3} ÷ x = \dfrac{301}{48}÷\dfrac{83}{48} $

$\small\text{ora moltiplica gli estremi e dividi per il medio noto:}$

$\small x= \dfrac{\dfrac{\cancel2^1}{3}·\dfrac{83}{\cancel{48}_{24}}}{\dfrac{301}{48}} $

$\small x= \dfrac{1}{3}·\dfrac{83}{\cancel{24}_1}·\dfrac{\cancel{48}^2}{301} $

$\small x= \dfrac{1}{3}·\dfrac{83}{1}·\dfrac{2}{301} $

$\small x= \dfrac{166}{903} $