Odpowiedź:
[tex]x=0.(6)\\10x=6.(6)\\10x-x=6.(6)-0.(6)\\9x=6\\x=\frac{6}{9} =\frac{2}{3}[/tex]
[tex]y=4.(36)\\100y=436.(36)\\100y-y=436.(36)-4.(36)\\99y=432\\y=\frac{432}{99} =\frac{48}{11}[/tex]
[tex]x+y=\frac{2}{3} +\frac{48}{11} =\frac{22}{33} +\frac{144}{33} =\frac{166}{33}[/tex]
[tex]x^{2} -y=(\frac{2}{3} )^{2}-\frac{48}{11}=\frac{4}{9}-\frac{48}{11}=\frac{44}{99}- \frac{432}{99}= -\frac{388}{99}[/tex]
[tex]x+\frac{1}{y} =\frac{2}{3} +\frac{1}{\frac{48}{11} } =\frac{2}{3}+\frac{11}{48}=\frac{32}{48}+\frac{11}{48}=\frac{43}{48}[/tex]
