Question

CMR: P/S A= \(\dfrac{12n+1}{30n+2}\) (n∈N) là P/S tối giản

Answer 1

Gọi ƯCLN\(\left(12n+1;30n+2\right)=d\)

\(\Rightarrow\left\{{}\begin{matrix}\left(12n+1\right)⋮d\\\left(30n+2\right)⋮d\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}\left(60n+5\right)⋮d\\\left(60n+4\right)⋮d\end{matrix}\right.\)

\(\Rightarrow\left(60n+5\right)-\left(60n+4\right)⋮d\)

\(\Rightarrow1⋮d\)

\(\Rightarrow d\inƯ\left(1\right)\)

\(\Rightarrow d=1\)

Vì d = 1 \(\Rightarrow\dfrac{12n+1}{30n+2}\) là phân số tối giản.