Final answer:
To solve the expression 5/6x - 5/12x - 1/3 + 1/4x + 1/12, combine like terms and simplify the fractions. The simplified expression is (5/18)x + (1/12).
Step-by-step explanation:
To solve the expression: 5/6x - 5/12x - 1/3 + 1/4x + 1/12, we need to combine like terms. First, combine the terms with x: 5/6x - 5/12x + 1/4x. We can find the common denominator by multiplying the denominators (6, 12, and 4) to get 24. Then, multiply each fraction by the appropriate factor to have a denominator of 24:
(40/72)x - (20/72)x + (6/24)x + (2/24)
Now, we can combine the numerators: (40/72 - 20/72 + 6/24)x + (2/24)
Simplify the numerators: (20/72)x + (2/24)
Now, we can simplify the fractions by dividing the numerator and denominator by their greatest common factor:
(5/18)x + (1/12)