What is the value of (3 rac15 - 1 rac13) ext of rac14 ext divided by rac12?

$$3\frac{1}{5} = \frac{3 \times 5 + 1}{5} = \frac{16}{5}$$ $$1\frac{1}{3} = \frac{1 \times 3 + 1}{3} = \frac{4}{3}$$

Find a common denominator for 5 and 3, which is 15.

$$\frac{16}{5} - \frac{4}{3} = \frac{16 \times 3}{5 \times 3} - \frac{4 \times 5}{3 \times 5} = \frac{48}{15} - \frac{20}{15} = \frac{48 - 20}{15} = \frac{28}{15}$$

$$\frac{28}{15} \text{ of } \frac{1}{4} = \frac{28}{15} \times \frac{1}{4}$$

Multiply the numerators and the denominators.

$$\frac{28 \times 1}{15 \times 4} = \frac{28}{60}$$

Simplify the fraction by dividing both numerator and denominator by their greatest common divisor, which is 4.

$$\frac{28 \div 4}{60 \div 4} = \frac{7}{15}$$

$$\frac{7}{15} \div \frac{1}{2}$$

To divide by a fraction, multiply by its reciprocal.

$$\frac{7}{15} \times \frac{2}{1} = \frac{7 \times 2}{15 \times 1} = \frac{14}{15}$$

The final answer is $\frac{14}{15}$.