Cho \[n \in \mathbb{N}\]. Chứng tỏ rằng phân số \(\frac{{14n + 3}}{{21n + 5}}\) là phân số tối giản.

a) \(\frac{2}{5} - \frac{1}{5}.\frac{3}{{ - 4}}\)

\( = \frac{2}{5} - \frac{3}{{ - 20}}\)

\( = \frac{8}{{20}} + \frac{3}{{20}}\)

\( = \frac{{11}}{{20}}\);

b) \[\frac{{ - 3}}{4}.\frac{{2022}}{{2023}} - \frac{{2022}}{{2023}}.\frac{1}{4}\]

\[ = \frac{{2022}}{{2023}}.\left( {\frac{{ - 3}}{4} - \frac{1}{4}} \right)\]

\[ = \frac{{2022}}{{2023}}.\left( { - 1} \right)\]

\[ =  - \frac{{2022}}{{2023}}\];

c) \(1,25:\frac{{15}}{{20}} + \left( {25\%  - \frac{5}{6}} \right):4\frac{2}{3}\)

\( = \frac{{125}}{{100}}:\frac{3}{4} + \left( {\frac{{25}}{{100}} - \frac{5}{6}} \right):\frac{{14}}{3}\)

\( = \frac{6}{5}.\frac{4}{3} + \left( {\frac{1}{4} - \frac{5}{6}} \right).\frac{3}{{14}}\)

\( = \frac{8}{5} + \left( {\frac{3}{{12}} - \frac{{10}}{{12}}} \right).\frac{3}{{14}}\)

\( = \frac{8}{5} + \frac{{ - 7}}{{12}}.\frac{3}{{14}}\)

\( = \frac{8}{5} + \frac{{ - 1}}{8} = \frac{{64}}{{40}} - \frac{5}{{40}} = \frac{{59}}{{40}}\).