Question

aratati ca fractia 4n+3supra 6n+4 este ireductibila oricare arfi n apartinand nr naturale (N)

Answer 1

[tex]\text{Fie~d~nr.~cu~care~simplificam~astfel~incat:}~ \\ d~|~4n+3 \\ ~\text{si}~ \\ d~|~6n+4. \\ \\ d~|~4n+3/\cdot3 \Rightarrow d~|~12n+9~(1) \\ d~|~6n+4/\cdot2\Rightarrow d~|~12n+8~(2)\\ \\ \text{Din}~(1)~\text{si}~(2)\Rightarrow \text{d~divide~si~diferenta}\Rightarrow \\ d~|~12n+9-12n-8\Rightarrow d~|~1\Rightarrow \boxed{d=1}\Rightarrow \text{Fractia~este~ireductibila.}[/tex]