Simplify Expression D1Caea

1. **State the problem:** Simplify the expression $$a + \frac{3}{4} b - \frac{5}{6} b$$. 2. **Identify like terms:** The terms involving $$b$$ are $$\frac{3}{4} b$$ and $$-\frac{5}{6} b$$. 3. **Find common denominator for fractions:** The denominators are $$4$$ and $$6$$. The least common denominator (LCD) is $$12$$. 4. **Convert fractions to have the LCD:** $$\frac{3}{4} b = \frac{3 \times 3}{4 \times 3} b = \frac{9}{12} b$$ $$-\frac{5}{6} b = -\frac{5 \times 2}{6 \times 2} b = -\frac{10}{12} b$$ 5. **Combine the $$b$$ terms:** $$\frac{9}{12} b - \frac{10}{12} b = \frac{9 - 10}{12} b = -\frac{1}{12} b$$ 6. **Write the simplified expression:** $$a - \frac{1}{12} b$$ **Final answer:** $$a - \frac{1}{12} b$$