implify the following expressi \( \frac{x+2}{3}-\frac{x-1}{4}-\frac{5}{12} \)

To simplify the expression \( \frac{x+2}{3} - \frac{x-1}{4} - \frac{5}{12} \), we first need a common denominator. The least common multiple of 3, 4, and 12 is 12. Now, we can rewrite each fraction with a denominator of 12: - \( \frac{x+2}{3} = \frac{4(x+2)}{12} = \frac{4x + 8}{12} \) - \( \frac{x-1}{4} = \frac{3(x-1)}{12} = \frac{3x - 3}{12} \) - \( \frac{5}{12} = \frac{5}{12} \) Now substituting these back into the expression gives: \[ \frac{4x + 8}{12} - \frac{3x - 3}{12} - \frac{5}{12} \] Combine the numerators: \[ \frac{(4x + 8) - (3x - 3) - 5}{12} \] This simplifies to: \[ \frac{4x + 8 - 3x + 3 - 5}{12} = \frac{x + 6}{12} \] So the simplified expression is: \[ \frac{x + 6}{12} \]