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

a) \[3,22 + 10,78 - 3,14\].

\[ = \left( {3,22 + 10,78} \right) - 3,14\]

\[ = 14 - 3,14\]

\[ = 10,86\].

c) \[20\%  - \frac{1}{2}:\frac{3}{4} + 0,2.\frac{{ - 2}}{3}\].

\[ = \frac{1}{5} - \frac{2}{3} + \frac{1}{5}.\frac{{ - 2}}{3}\]

\[ = \frac{1}{5} - \frac{2}{3} + \frac{{ - 2}}{{15}}\]

\[ = \frac{{ - 3}}{5}\].

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

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

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

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

d) \[\frac{6}{{11}}.\frac{8}{{15}} + \frac{6}{{11}}.\frac{7}{{15}} + \frac{{ - 5}}{{11}}\]

\[ = \frac{6}{{11}}.\left( {\frac{8}{{15}} + \frac{7}{{15}}} \right) + \frac{{ - 5}}{{11}}\]

\[ = \frac{6}{{11}}.1 + \frac{{ - 5}}{{11}}\]

\[ = \frac{6}{{11}} + \frac{{ - 5}}{{11}}\]

\[ = \frac{1}{{11}}\].