Final answer:
To solve the expression (3x + 2/3 ÷ -x - 1/4 ÷ -5/12), you need to follow the order of operations and simplify the divisions and multiplications, and then combine like terms.
Step-by-step explanation:
To solve the expression (3x + 2/3 ÷ -x - 1/4 ÷ -5/12), you need to follow the order of operations, which is also known as the PEMDAS rule. PEMDAS stands for Parentheses, Exponents, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Let's break down the expression step-by-step:
1. Start by simplifying the divisions from left to right:
3x + (2/3) ÷ (-x) - (1/4) ÷ (-5/12)
2. Simplify each division:
3x + (2/3) * (-1/x) - (1/4) * (-12/5)
3. Simplify the multiplications:
3x - 2/3x - 12/20
4. Combine like terms:
(9x^2 - 6 - 36x)/(20x)
So, the simplified expression is (9x^2 - 36x - 6)/(20x).
The answer cannot be determined without more information about the value of x.