3. \( -3 \frac{1}{4} \div\left(-2 \frac{2}{5}\right)+\left(-\frac{3}{7}\right) \)

To solve the expression \( -3 \frac{1}{4} \div\left(-2 \frac{2}{5}\right)+\left(-\frac{3}{7}\right) \), we first convert the mixed numbers into improper fractions. For \( -3 \frac{1}{4} \): \[ -3 \frac{1}{4} = -\left(3 \times 4 + 1\right)/4 = -\frac{13}{4} \] For \( -2 \frac{2}{5} \): \[ -2 \frac{2}{5} = -\left(2 \times 5 + 2\right)/5 = -\frac{12}{5} \] Now we have the expression: \[ -\frac{13}{4} \div -\frac{12}{5} + \left(-\frac{3}{7}\right) \] Dividing by a fraction is the same as multiplying by its reciprocal, so: \[ -\frac{13}{4} \div -\frac{12}{5} = -\frac{13}{4} \times -\frac{5}{12} = \frac{13 \times 5}{4 \times 12} = \frac{65}{48} \] Now, we add \( -\frac{3}{7} \): \[ \frac{65}{48} + \left(-\frac{3}{7}\right) \] To add these fractions, we need a common denominator. The least common multiple of 48 and 7 is 336. Converting both fractions: \[ \frac{65}{48} = \frac{65 \times 7}{48 \times 7} = \frac{455}{336} \] \[ -\frac{3}{7} = -\frac{3 \times 48}{7 \times 48} = -\frac{144}{336} \] Now adding: \[ \frac{455}{336} - \frac{144}{336} = \frac{455 - 144}{336} = \frac{311}{336} \] Thus, the final answer is: \[ \frac{311}{336} \]