Explicație pas cu pas:
legea * este asociativă:
[tex]1*2 = \frac{3 \times 1 \times 2 + 1}{1 + 2} = \frac{6 + 1}{3} = \frac{7}{3} [/tex]
[tex]((1*2)*3) = \frac{7}{3} *3 = \frac{3 \times \frac{7}{3} \times 3 + 1 }{ \frac{7}{3} + 3} = \frac{21 + 1}{ \frac{7 + 9}{3} } = \frac{22 \times 3}{16} = \frac{33}{8} [/tex]
[tex]2*3= \frac{3 \times 2 \times 3 + 1}{2 + 3} = \frac{18 + 1}{5} = \frac{19}{5} [/tex]
[tex]1*(2*3)=1* \frac{19}{5} = \frac{3 \times 1 \times \frac{19}{5} + 1 }{1 + \frac{19}{5} } = \frac{57 + 5}{5 + 19} = \frac{62}{24 }[/tex]
deci:
[tex]((1*2)*3)-(1*(2*3))= \frac{33}{8} - \frac{62}{24} = \frac{33 \times3 - 62}{24} = \frac{99 - 62}{24} = \frac{37}{24} [/tex]
