a, Gọi WCLN (n+1;2n+3)=d
\(\Rightarrow\)\(\left\{{}\begin{matrix}n+1:d\\2n+3:d\end{matrix}\right.\)\(\Rightarrow\)\(\left\{{}\begin{matrix}2.\left(n+1\right):d\\2n+3:d\end{matrix}\right.\)\(\Rightarrow\)\(\left\{{}\begin{matrix}2n+2:d\\2n+3:d\end{matrix}\right.\)
\(\Rightarrow\)(2n+3)-(2n+2):d
\(\Rightarrow\)2n+3-2n-2 :d
\(\Rightarrow\)1:d\(\frac{ }{\Rightarrow}\)d\(\in\) Ư (1;-1)
\(\Rightarrow\)n+1;2n+3 là số nguyên tố
Vậy \(\frac{n+1}{2n+3}\)là vân số tối giản
b,Gọi UCLN (2n+3;4n+7)=d
\(\Rightarrow\)\(\left\{{}\begin{matrix}2n+3:d\\4n+7:d\end{matrix}\right.\)\(\Rightarrow\)\(\left\{{}\begin{matrix}2\left(2n+3\right):d\\4n+7:d\end{matrix}\right.\)\(\Rightarrow\)\(\left\{{}\begin{matrix}4n+6:d\\4n+7:d\end{matrix}\right.\)
\(\Rightarrow\)(4n+7)-(4n+6):d
\(\Rightarrow\)4n+7-4n-6:d
\(\Rightarrow\)1:d \(\Rightarrow\)d\(\in\)Ư (1)
\(\Rightarrow\)2n+3;4n+7 là số nguyên tố
Vậy\(\frac{2n+3}{4n+7}\)là phân số tối giản
