Question

Aratati ca x,(y)+y,(x)=x,y(x)+y,x(y)=x,(yx)+y,(xy)

Answer 1

x,(y)+y,(x)=(10x+y-x)/9+(10y+x-y)/9=(9x+y+9y+x)/9=10(x+y)/9

x,y(x)+y,x(y)=(100x+10y+x-10x-y)/90+(100y+10x+y-10y-x)/90= =(91x+9y+91y+9x)/90=100(x+y)/90=10(x+y)/9

x,(yx)+y,(xy) =(100x+10y+x-x)/99+(100y+10x+y-y)/99=
=(100x+10y+100y+10x)/99=(110x+110y)/99=110(x+y)/99=10(x+y)/9

rezulta ca:
x,(y)+y,(x)=x,y(x)+y,x(y)=x,(yx)+y,(xy) =10(x+y)/9