Find the Common Factor in (2x/b + 4c/3b): Step-by-Step Solution

To solve this problem, we will follow the steps below:

Let's start by examining the given expression:

$\frac{2x}{b} + \frac{4c}{3b}$

Step 1: Identify the common factor in both terms.

Both terms have a denominator of $b$. We can factor $\frac{1}{b}$ out of the entire expression.

Step 2: Factor out the common factor.

$\frac{2x}{b} = \frac{1}{b} \cdot 2x$
$\frac{4c}{3b} = \frac{1}{b} \cdot \frac{4c}{3}$

Step 3: Combine terms using the common factor.

Now, factor $\frac{1}{b}$ out of the expression:
$\frac{1}{b}(2x + \frac{4c}{3})$

Step 4: Simplify the expression.

We notice that both terms have a common factor of 2 in the numerators:

$\frac{1}{b} \cdot (2x + \frac{4c}{3}) = \frac{2}{b} \cdot (x + \frac{2c}{3})$

Therefore, the common factor in the expression is $\frac{2}{b}(x+\frac{2c}{3})$.