c) \( \frac{\frac{1}{3}-\frac{5}{6}}{\frac{2}{3}+\frac{5}{12}}= \)

To solve the expression \( \frac{\frac{1}{3}-\frac{5}{6}}{\frac{2}{3}+\frac{5}{12}} \), we first handle the numerator. We need a common denominator to subtract \(\frac{1}{3}\) and \(\frac{5}{6}\). The common denominator is 6, so: \[ \frac{1}{3} = \frac{2}{6} \] Thus, we can write: \[ \frac{1}{3} - \frac{5}{6} = \frac{2}{6} - \frac{5}{6} = \frac{2 - 5}{6} = \frac{-3}{6} = -\frac{1}{2} \] Next, we simplify the denominator \(\frac{2}{3} + \frac{5}{12}\). The common denominator here is 12: \[ \frac{2}{3} = \frac{8}{12} \] Now we can add: \[ \frac{2}{3} + \frac{5}{12} = \frac{8}{12} + \frac{5}{12} = \frac{8 + 5}{12} = \frac{13}{12} \] Now we plug these results back into the original expression: \[ \frac{-\frac{1}{2}}{\frac{13}{12}} = -\frac{1}{2} \times \frac{12}{13} = -\frac{12}{26} = -\frac{6}{13} \] So the final answer is: \[ -\frac{6}{13} \]