Final answer:
The simplified equivalent expression to the given problem (-7/6t + 4/9) - (-5/12t + 2/3) is -1/3t - 2/9 after combining like terms and simplifying.
Step-by-step explanation:
The expression given is (-7/6t + 4/9) - (-5/12t + 2/3). To simplify this expression, we subtract each term in the second parentheses from the corresponding term in the first parentheses, and change the sign of each term in the second parentheses because of the minus sign before it.
First, simplify the t terms:
- (-7/6)t - (-5/12)t
- = (-7/6)t + (5/12)t
Find a common denominator for the fractions, which is 12, and combine:
- =(12[-7 + 5]) / (6*12)
- = -14/12t + 10/12t
- = -4/12t
- = -1/3t (simplifying the fraction by dividing both the numerator and denominator by 4)
Now, simplify the constant terms:
- 4/9 - 2/3
- =(4/9) - (6/9)
- = -2/9 (combining the fractions)
Combine the simplified t term and the constant:
Therefore, the equivalent expression is -1/3t - 2/9.