Question

CM:(10n^2+9n+4)/(20n^2+20n+9) ko tối giản

Answer 1

\(\dfrac{10n^2+9n+4}{20n^2+20n+9}\)

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 .