Decompose the Expression: xy/2 + x/4y into Factors

To factor the expression $\frac{xy}{2}+\frac{x}{4y}$, we proceed as follows:

• Step 1: Identify the common factor between the terms.
• Step 2: Factor out the common factor.
• Step 3: Simplify the expression inside the parentheses.

Let's break this down:
Step 1: The expression is $\frac{xy}{2} + \frac{x}{4y}$. Clearly, both terms share $\frac{x}{2}$ as a common factor.
Step 2: Factor out $\frac{x}{2}$ from each term:
- From the first term: $\frac{xy}{2} = \frac{x}{2} \times y$.
- From the second term: $\frac{x}{4y} = \frac{x}{2} \times \frac{1}{2y}$.
Step 3: This gives us:
$\frac{xy}{2} + \frac{x}{4y} = \frac{x}{2}(y + \frac{1}{2y})$

Thus, the expression can be decomposed into factors as $\frac{x}{2}(y+\frac{1}{2y})$.