Buongiorno,potreste aiutarmi con la verifica di quest’equazione?Grazie sempre

S = (-6 + 2)/3 - (-6 + 11)/2 = -4/3 - 5/2 = (-8 - 15)/6 = -23/6 ;

D = 3/2 * ((2+6)/2 - 6) - 5/6 = 3/2 *(-2) - 5/6 = -3 - 5/6 = (-18 - 5)/6 = -23/6.

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$\small \dfrac{x+2}{3} -\dfrac{x+11}{2} = \dfrac{3}{2}\left(\dfrac{2-x}{2}+x\right)-\dfrac{5}{6}$

$\small \dfrac{x+2}{3} -\dfrac{x+11}{2} = \dfrac{3}{2}·\dfrac{2-x}{2}+\dfrac{3}{2}·x-\dfrac{5}{6}$

$\small \dfrac{x+2}{3} -\dfrac{x+11}{2} = \dfrac{3}{4}(2-x)+\dfrac{3}{2}x-\dfrac{5}{6}$ mcm=12

$\small 4(x+2) -6(x+11) = 9(2-x)+18x-10$

$\small 4x+8-6x-66 = 18-9x+18x-10$

$\small -2x-58 = 9x+8$

$\small -2x-9x = 8+58$

$\small -11x = 66$

$\small 11x = -66$

$\small \dfrac{\cancel{11}x}{\cancel{11}} = \dfrac{-66}{11}$

$\small x= -6$

verifica sostituendo il valore trovato all'incognita:

$\small \dfrac{-6+2}{3} -\dfrac{-6+11}{2} = \dfrac{3}{2}\left(\dfrac{2-(-6)}{2}+(-6)\right)-\dfrac{5}{6}$

$\small \dfrac{-4}{3} +\dfrac{5}{2} = \dfrac{3}{2}\left(\dfrac{2+6}{2}-6\right)-\dfrac{5}{6}$

$\small \dfrac{-8-15}{6}  = \dfrac{3}{2}\left(\dfrac{8}{2}-6\right)-\dfrac{5}{6}$

$\small \dfrac{-23}{6}  = \dfrac{3}{2}\left(4-6\right)-\dfrac{5}{6}$

$\small \dfrac{-23}{6}  = \dfrac{3}{\cancel2}\left(-\cancel2\right)-\dfrac{5}{6}$

$\small \dfrac{-23}{6}  = -3-\dfrac{5}{6}$

$\small \dfrac{-23}{6}  = \dfrac{-18-5}{6}$

$\small -\dfrac{23}{6}  = -\dfrac{23}{6}$  eguaglianza verificata.