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To combine the fractions \(\frac{5}{6x} + \frac{3}{4x}\), we first need to find a common denominator.

### Step 1: Identify the Least Common Denominator (LCD)
The denominators are \(6x\) and \(4x\). The least common denominator (LCD) will be the least common multiple (LCM) of 6 and 4, which is 12. Therefore, the LCD is \(12x\).

### Step 2: Rewrite the fractions with the LCD
We now rewrite both fractions so they have the common denominator \(12x\):
\[
\frac{5}{6x} = \frac{5 \times 2}{6x \times 2} = \frac{10}{12x}
\]
\[
\frac{3}{4x} = \frac{3 \times 3}{4x \times 3} = \frac{9}{12x}
\]

### Step 3: Combine the fractions
Now that both fractions have the same denominator, we can combine them:
\[
\frac{10}{12x} + \frac{9}{12x} = \frac{10 + 9}{12x} = \frac{19}{12x}
\]

### Step 4: Final expression
The result is:
\[
\frac{19}{12x}
\]
This fraction is already in its fully reduced form.

Would you like further details on any of these steps?

Here are some related questions for practice:
1. How do you find the least common denominator between two fractions?
2. What are the steps to add fractions with different denominators?
3. How would the problem change if one denominator were \(6x^2\) instead of \(6x\)?
4. How do you reduce a fraction to its simplest form?
5. What happens if you subtract the fractions instead of adding them?

**Tip**: Always check if the resulting fraction can be simplified after combining fractions.

Combine the following fractions and express in fully reduced form: 5/(6x) + 3/(4x).

Learn how to combine algebraic fractions like 5/(6x) + 3/(4x) using the least common denominator (LCD) method. This problem focuses on adding fractions with different denominators, suitable for students in Grades 6-8.

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