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The expression you are working with is:

\[
\frac{5}{4x} + \frac{3}{8x}
\]

The task asks to add these terms together using **8x** as the common denominator.

### Step-by-Step Solution:

1. **Find the common denominator:**  
   The denominators are \(4x\) and \(8x\). A common denominator is **8x**, as stated in the problem.

2. **Rewrite the fractions with the common denominator:**  
   The first term \(\frac{5}{4x}\) needs to be rewritten with \(8x\) as the denominator. To do that, multiply both the numerator and denominator of the first fraction by 2:
   \[
   \frac{5}{4x} = \frac{5 \times 2}{4x \times 2} = \frac{10}{8x}
   \]

   The second term already has the denominator \(8x\), so it remains the same:
   \[
   \frac{3}{8x}
   \]

3. **Add the two fractions:**  
   Now that both fractions have the same denominator, simply add the numerators:
   \[
   \frac{10}{8x} + \frac{3}{8x} = \frac{10 + 3}{8x} = \frac{13}{8x}
   \]

Thus, the result of adding \(\frac{5}{4x} + \frac{3}{8x}\) with a common denominator of \(8x\) is:

\[
\frac{13}{8x}
\]

Would you like more details or have any questions?

Here are 5 follow-up questions to expand on this topic:
1. How do you find the least common denominator for two fractions?
2. What happens if the terms have different variables in the denominator?
3. Can you simplify fractions when the denominator includes variables?
4. What if one of the terms in the expression has a negative sign?
5. How would you handle adding fractions where the denominator is more complex, such as binomials?

**Tip:** When adding fractions with different denominators, always find the least common denominator (LCD) to simplify the process of addition.

Consider the following expression: 5/(4x) + 3/(8x). Using 8x as the common denominator, add the terms together and show your calculations.

Learn how to add the fractions 5/(4x) + 3/(8x) by finding the common denominator. This algebra problem covers fraction addition, least common denominators, and variable expressions. Suitable for Grades 6-8 students.

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