Combine the following fractions and express in fully reduced form.
start fraction, 7, x, divided by, 6, end fraction, plus, start fraction, 9, x, divided by, 4, end fraction
6
7x
​
 + 
4
9x
​


To combine the fractions \(\frac{7x}{6} + \frac{9x}{4}\), we need to follow these steps:

### Step 1: Find the least common denominator (LCD)
The denominators are 6 and 4. The least common denominator of 6 and 4 is 12.

### Step 2: Rewrite the fractions with the LCD
- \(\frac{7x}{6} = \frac{7x \times 2}{6 \times 2} = \frac{14x}{12}\)
- \(\frac{9x}{4} = \frac{9x \times 3}{4 \times 3} = \frac{27x}{12}\)

### Step 3: Add the fractions
Now that both fractions have the same denominator, we can combine them:
\[
\frac{14x}{12} + \frac{27x}{12} = \frac{14x + 27x}{12} = \frac{41x}{12}
\]

### Step 4: Simplify
Since \(\frac{41x}{12}\) is already in its simplest form (no common factors between 41 and 12), the final answer is:

\[
\frac{41x}{12}
\]

Let me know if you would like any further details or explanations!

Here are 5 related questions you might find interesting:
1. How do you find the least common denominator of any two numbers?
2. How do you subtract fractions with different denominators?
3. Can you combine fractions with variables in both the numerator and denominator?
4. What are the rules for simplifying fractions?
5. How do you solve fractional equations involving variables?

**Tip:** When adding or subtracting fractions, always remember to first find a common denominator before performing the operation.

Combine the following fractions and express in fully reduced form: 7x/6 + 9x/4

Learn how to combine fractions with variables, such as 7x/6 and 9x/4, by finding the least common denominator and simplifying the result. This step-by-step guide is ideal for students in Grades 8-10 and covers key algebraic concepts.

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