\(\dfrac{10n^2+9n+4}{20n^2+20n+9}\)
Gỉa sử :
\(\left\{{}\begin{matrix}10n^2+9n+4⋮d\\20n^2+20n+9⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}20n^2+18n+8⋮d\\20n^2+20n+9⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2n+1⋮d\\10n^2+9n+4⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}10n^2+5n⋮d\\10n^2+9n+4⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4n+4⋮d\\10n^2+5n⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4n+4⋮d\\2n+1⋮d\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}4n+4⋮d\\4n+2⋮d\end{matrix}\right.\)
\(\Leftrightarrow2⋮d\)
Vậy phân số trên chưa tối giản .
