To subtract 12(z + 4) - 3(14z + 1) using fractions, we need to distribute the coefficients to each term within the parentheses and then combine like terms.
First, let's distribute 12 to the terms inside the first set of parentheses:
12(z + 4) = 12z + 12(4) = 12z + 48
Next, let's distribute -3 to the terms inside the second set of parentheses:
-3(14z + 1) = -3(14z) + (-3) = -42z - 3
Now we can subtract the two expressions:
12z + 48 - (-42z - 3)
To subtract a negative, we change the signs within the parentheses:
12z + 48 + 42z + 3
Combining like terms, we get:
(12z + 42z) + (48 + 3) = 54z + 51
Therefore, the final result in fraction form is 54z + 51.