a/ Gọi \(d=ƯCLN\left(4n+3;10n+7\right)\)
\(\Rightarrow\left\{{}\begin{matrix}4n+3⋮d\\10n+7⋮d\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}20n+15⋮d\\20n+14⋮d\end{matrix}\right.\)
\(\Rightarrow\left(20n+15\right)-\left(20n+14\right)⋮d\)
\(\Rightarrow1⋮d\Rightarrow d=1\)
\(\Rightarrow\frac{4n+3}{10n+7}\) là phân số tối giản
b/ Gọi \(d=ƯCLN\left(2n+3;4n+8\right)\)
Do \(2n+3\) lẻ với mọi n tự nhiên \(\Rightarrow d\) lẻ
\(\left\{{}\begin{matrix}2n+3⋮d\\4n+8⋮d\end{matrix}\right.\) \(\Rightarrow\left\{{}\begin{matrix}4n+6⋮d\\4n+8⋮d\end{matrix}\right.\)
\(\Rightarrow\left(4n+8\right)-\left(4n+6\right)⋮d\)
\(\Rightarrow2⋮d\Rightarrow d=\left\{1;2\right\}\)
Mà \(d\) lẻ \(\Rightarrow d=1\)
\(\Rightarrow\frac{2n+3}{4n+8}\) tối giản
