Comprehensive Solution for the Expression $\frac{x}{2}(\frac{1}{4y}+\frac{5}{3a}+bc)$

Step 1: Identify the Expression

We are given the expression $\frac{x}{2}(\frac{1}{4y}+\frac{5}{3a}+bc)$.

Step 2: Distribute $\frac{x}{2}$ to Each Term Inside the Parentheses

Our next step is to apply the distributive property to eliminate the parentheses. We will multiply $\frac{x}{2}$ by each term inside $\frac{1}{4y}+\frac{5}{3a}+bc$.

Expression: $\frac{x}{2}\times \frac{1}{4y}+\frac{x}{2}\times \frac{5}{3a}+\frac{x}{2}\times bc$

Step 3: Simplify Each Term

Now, we will simplify each term by multiplying the fractions.

First Term: $\frac{x}{2}\times \frac{1}{4y}=\frac{x}{8y}$

Second Term: $\frac{x}{2}\times \frac{5}{3a}=\frac{5x}{6a}$

Third Term: $\frac{x}{2}\times bc=\frac{bcx}{2}$

Step 4: Combine the Simplified Terms

Finally, we combine all the simplified terms to get the final expression.

Combined Expression: $\frac{x}{8y}+\frac{5x}{6a}+\frac{bcx}{2}$

Conclusion: The simplified expression for $\frac{x}{2}(\frac{1}{4y}+\frac{5}{3a}+bc)$ is $\frac{x}{8y}+\frac{5x}{6a}+\frac{bcx}{2}$.