bai 39
Giả sử ƯCLN(12n+1,20n+2)=d (d \(\in\) N)
\(\Rightarrow\)(12n+1) \(⋮\) d \(\Rightarrow\) 5.(12n+1) \(⋮\) d
\(\Rightarrow\)(30n+2) \(⋮\) d \(\Rightarrow\) 2.(30n+2) \(⋮\) d
\(\Rightarrow\)5.(12n+1) - 2.(30n+2) \(⋮\) d= (60n-60n)+(5-4)=0+1=1
5.(12n+1)\(⋮\) d suy chung ra 2 biểu thức 5.(12n+1)-2.(30n+2)=1 \(⋮\) d\(\Rightarrow\)d=1
2.(30n+2) \(⋮\) d
d=1 \(\Rightarrow\)\(\frac{12n+1}{30n+2}\) tối giản
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