14-13,2:(3 11/21-2 7/15)

To simplify the expression \(14 - \frac{13}{2} : \left(3\frac{11}{21} - 2\frac{7}{15}\right)\), we will first convert the mixed numbers to improper fractions:

\[14 - \frac{13}{2} : \left(3\frac{11}{21} - 2\frac{7}{15}\right)\]

\[= 14 - \frac{13}{2} : \left(\frac{64}{21} - \frac{37}{15}\right)\]

Next, we convert the division into multiplication by taking the reciprocal of the divisor:

\[= 14 - \frac{13}{2} \times \left(\frac{64}{21} - \frac{37}{15}\right)\]

Now we multiply the fractions inside the parenthesis:

\[= 14 - \frac{13}{2} \times \left(\frac{64}{21} - \frac{37}{15}\right)\]

\[= 14 - \frac{13}{2} \times \left(\frac{64 \times 15}{21 \times 15} - \frac{37 \times 21}{15 \times 21}\right)\]

\[= 14 - \frac{13}{2} \times \left(\frac{960}{315} - \frac{777}{315}\right)\]

\[= 14 - \frac{13}{2} \times \left(\frac{960 - 777}{315}\right)\]

\[= 14 - \frac{13}{2} \times \left(\frac{183}{315}\right)\]

\[= 14 - \frac{13 \times 183}{2 \times 315}\]

\[= 14 - \frac{2379}{630}\]

Now we subtract the fractions:

\[= \frac{8820 - 2379}{630}\]

\[= \frac{6441}{630}\]

Now we can simplify the fraction by finding the greatest common divisor of 6441 and 630, which is 63:

\[\frac{6441}{630} = \frac{6441 \div 63}{630 \div 63} = \frac{103}{10}\]

Therefore, the simplified expression is \(\frac{103}{10}\).