N° 937

(5-1/3x3/2+x)÷x=(5/2+1/3+3/2x4/3)÷(5+1/3-3/2x4/3); proporzione;

(5 -1/3 * 3/2 + x) =

= 5 - 1/2 + x = 10/2 - 1/2 + x = 9/2 + x;

primo rapporto a sinistra dell'uguale diventa:

(9/2 + x) : x ;

secondo rapporto a destra:

(5/2 + 1/3 + 3/2 * 4/3) ÷ (5 + 1/3 - 3/2 * 4/3) =

= (5/2 + 1/3 + 2/1) : (5 + 1/3 - 2/1) =

= (15/6 + 2/6 + 12/6) : (15/3 + 1/3 - 6/3) =

= 29/6 : 10/3;

(9/2 + x) : x = 29/6 : 10/3;  scomporre:

(9/2 + x - x) : x = (29/6 - 10/3) : 10/3;

9/2 : x = (29/6 - 20/6) : 10/3;

9/2 : x = 9/6 : 10/3;

9/2 : x = 3/2 : 10/3;

x = 9/2 * 10/3 * 2/3;

x = 1/1 * 10/1 * 1/1;

x = 10;

infatti:

9/2 : 10 = 3/2 : 10/3;

9/2 * 1/10 = 9/20;  (1)

3/2 * 3/10 = 9/20;  (2)

(5-1/3x3/2+x)÷x=(5/2+1/3+3/2x4/3)÷(5+1/3-3/2x4/3)

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$\small\left(5-\dfrac{1}{\cancel3_1}·\dfrac{\cancel3^1}{2}+x\right)÷x = \left(\dfrac{5}{2}+\dfrac{1}{3}+\dfrac{\cancel3^1}{\cancel2_1}·\dfrac{\cancel4^2}{\cancel3_1}\right)÷\left(5+\dfrac{1}{3}-\dfrac{\cancel3^1}{\cancel2_1}·\dfrac{\cancel4^2}{\cancel3_1}\right)$

$\small\left(5-\dfrac{1}{2}+x\right)÷x = \left(\dfrac{5}{2}+\dfrac{1}{3}+2\right)÷\left(5+\dfrac{1}{3}-2\right)$

$\small\left(\dfrac{10-1}{2}+x\right)÷x = \left(\dfrac{15+2+12}{6}\right)÷\left(\dfrac{15+1-6}{3}\right)$

$\small\left(\dfrac{9}{2}+x\right)÷x = \dfrac{29}{6}÷\dfrac{10}{3}$

$\small\text{applica lo scomporre:}$

$\small\left(\dfrac{9}{2}+x-x\right)÷x = \left(\dfrac{29}{6}-\dfrac{10}{3}\right)÷\dfrac{10}{3}$

$\small\left(\dfrac{9}{2}+\cancel{x}-\cancel{x}\right)÷x = \left(\dfrac{29-20}{6}\right)÷\dfrac{10}{3}$

$\small\dfrac{9}{2}÷x = \dfrac{\cancel9^3}{\cancel6_2}÷\dfrac{10}{3}$

$\small\dfrac{9}{2}÷x = \dfrac{3}{2}÷\dfrac{10}{3}$

$\small x= \dfrac{\cancel9^3}{\cancel2_1}·\dfrac{\cancel{10}^5}{\cancel3_1}÷\dfrac{3}{2}$

$\small x= 3·5·\dfrac{2}{3}$

$\small x= \cancel{15}^5·\dfrac{2}{\cancel3_1}$

$\small x= 5·2$

$\small x= 10$