To solve the rational function \( \frac{X}{9} - \frac{2}{5} = \frac{1}{3} \), let's follow these steps:

### Step 1: Eliminate the denominators
To eliminate the denominators (9, 5, and 3), we multiply through by the least common denominator (LCD) of 9, 5, and 3. The LCD of 9, 5, and 3 is 45.

So, multiply each term by 45:

\[
45 \times \left( \frac{X}{9} \right) - 45 \times \left( \frac{2}{5} \right) = 45 \times \left( \frac{1}{3} \right)
\]

### Step 2: Simplify
Now simplify each term:

\[
\frac{45X}{9} - \frac{90}{5} = \frac{45}{3}
\]

This becomes:

\[
5X - 18 = 15
\]

### Step 3: Solve for \( X \)
Now, solve for \( X \):

\[
5X = 15 + 18
\]

\[
5X = 33
\]

\[
X = \frac{33}{5}
\]

So, the solution is:

\[
X = \frac{33}{5}
\]

Would you like further details or have any questions?

### Related questions:
1. How can we find the least common denominator in rational equations?
2. What happens when there are variables in both the numerator and the denominator?
3. How can you solve rational equations with multiple variables?
4. What if we had a quadratic equation instead of a linear one?
5. How can rational functions be applied in real-world problems?

**Tip:** When solving rational equations, always clear the denominators first to simplify the process.

Discover how to solve the rational function X/9 - 2/5 = 1/3 using the least common denominator method. This step-by-step solution simplifies the equation and demonstrates how to solve for X. Perfect for students in Grades 9-10.

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