20,375 cm

Xét$12n+1=12n+24-23=12\left(n+2\right)-23$

$\Rightarrow \genfrac{}{}{0ex}{}{12n+1}{2n\left(n+2\right)}=\genfrac{}{}{0ex}{}{12\left(n+2\right)-23}{2n\left(n+2\right)}=\genfrac{}{}{0ex}{}{12\left(n+2\right)}{2n\left(n+2\right)}-\genfrac{}{}{0ex}{}{23}{2n\left(n+2\right)}=\genfrac{}{}{0ex}{}{6}{n}-\genfrac{}{}{0ex}{}{23}{2n\left(n+2\right)}$

Xét$\genfrac{}{}{0ex}{}{23}{2n\left(n+2\right)}$ta có:

$2n\left(n+2\right)⋮2$

=> $2n\left(n+2\right)$là số chẵn

mà 23 là số lẻ

$\Rightarrow \genfrac{}{}{0ex}{}{23}{2n\left(n+2\right)}$Tối giản

$\Rightarrow \genfrac{}{}{0ex}{}{6}{n}-\genfrac{}{}{0ex}{}{23}{2n\left(n+2\right)}$tối giản

Vậy $\genfrac{}{}{0ex}{}{12n+1}{2n\left(n+2\right)}$Tối giản (ĐPCM)

:))))

Xét$12n+1=12n+24-23=12\left(n+2\right)-23$

$\Rightarrow \genfrac{}{}{0ex}{}{12n+1}{2n\left(n+2\right)}=\genfrac{}{}{0ex}{}{12\left(n+2\right)-23}{2n\left(n+2\right)}=\genfrac{}{}{0ex}{}{12\left(n+2\right)}{2n\left(n+2\right)}-\genfrac{}{}{0ex}{}{23}{2n\left(n+2\right)}=\genfrac{}{}{0ex}{}{6}{n}-\genfrac{}{}{0ex}{}{23}{2n\left(n+2\right)}$

Xét$\genfrac{}{}{0ex}{}{23}{2n\left(n+2\right)}$ta có:

$2n\left(n+2\right)⋮2$

=> $2n\left(n+2\right)$là số chẵn

mà 23 là số lẻ

$\Rightarrow \genfrac{}{}{0ex}{}{23}{2n\left(n+2\right)}$Tối giản

$\Rightarrow \genfrac{}{}{0ex}{}{6}{n}-\genfrac{}{}{0ex}{}{23}{2n\left(n+2\right)}$tối giản

Vậy $\genfrac{}{}{0ex}{}{12n+1}{2n\left(n+2\right)}$Tối giản (ĐPCM)