Simplify: 1/4 (6ab - 9b) + 2/3 (9ab + 12b)
To simplify the expression, we distribute the fractions to each term within the parentheses:
1/4 (6ab) - 1/4 (9b) + 2/3 (9ab) + 2/3 (12b)
This simplifies to:
(6/4)ab - (9/4)b + (18/3)ab + (24/3)b
Next, we simplify the fractions:
(3/2)ab - (9/4)b + (6)ab + (8)b
Now, we combine like terms:
(3/2 + 6)ab + (-9/4 + 8)b
This simplifies further to:
(15/2)ab + (23/4)b
Therefore, the simplified expression is 15/2ab + 23/4b.