Help proporzioni

33/14*7/3*x-x = 1/2

33x/6-x = 1/2

11x/2-x = 1/2

9x/2 = 1/2

x = 1/9

check

11/2 = (1/2+1/9)*9

11/2 = (9+2)/18*9

11/2 = 11/2

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$\small \left(\dfrac{1}{2}+x\right) : x = \dfrac{33}{14} : \dfrac{3}{7}$

applica la proprietà dello scomporre come segue:

$\small \left(\dfrac{1}{2}+x-x\right) : x = \left(\dfrac{33}{14}-\dfrac{3}{7}\right) : \dfrac{3}{7}$

$\small \left(\dfrac{1}{2}+\cancel{x}-\cancel{x}\right) : x = \left(\dfrac{33-6}{14}\right) : \dfrac{3}{7}$

$\small \dfrac{1}{2} : x = \dfrac{27}{14} : \dfrac{3}{7}$

$\small x= \dfrac{1}{2}·\dfrac{3}{7} : \dfrac{27}{14}$

$\small x= \dfrac{1}{2}·\dfrac{\cancel3^1}{\cancel7_1}·\dfrac{\cancel{14}^2}{\cancel{27}_9}$

$\small x= \dfrac{1}{\cancel2_1}·\dfrac{\cancel2^1}{9}$

$\small x= \dfrac{1}{9}; \quad(= 0,\overline1).$