Solve for Missing Values in 12ab(? + ?) = 24abc + 36

Fill in the missing values:

$12ab(?+?)=24abc+36$

To solve this problem, we'll rewrite the expression $12ab(?+?)=24abc+36$, focusing on the right-hand side, $24abc+36$.

Step 1: Factor the right-hand side:

Both terms on the right-hand side, $24abc$ and $36$, have a common factor. The greatest common factor (GCF) of $24abc$ and $36$ is $12$. Therefore, we can factor out $12$:

$24abc + 36 = 12(2ac + 3)$.

Step 2: Match the factored form with the left-hand side expression:

The equation now resembles $12ab(?+?) = 12(2ac + 3)$. To make the left-hand side equivalent to this expression, we equate it to the factorization result:

$12ab(?+?) = 12 \times (2ac + 3)$ implies $ab(?+?) = 2ac + 3$.

Step 3: Divide both sides by $ab$:

$? + ? = \frac{2ac}{ab} + \frac{3}{ab} = 2c + \frac{3}{ab}$.

Therefore, the missing values in the expression are $2c$ and $\frac{3}{ab}$.

Comparing this with the answer choices, the correct choice that aligns with these values is: $2c, \frac{3}{ab}$.

Therefore, the solution to the problem is $2c, \frac{3}{ab}$.