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The given equation is:

\[
\frac{x}{3} - \frac{x}{6} = \frac{5}{6}
\]

### Step 1: Find a Common Denominator

To simplify, find the least common denominator (LCD) of the fractions. The LCD of 3 and 6 is 6.

Rewrite the fractions with the common denominator:

\[
\frac{x}{3} = \frac{2x}{6}
\]

So the equation becomes:

\[
\frac{2x}{6} - \frac{x}{6} = \frac{5}{6}
\]

### Step 2: Combine the Fractions

Combine the fractions on the left side:

\[
\frac{2x - x}{6} = \frac{x}{6}
\]

So the equation simplifies to:

\[
\frac{x}{6} = \frac{5}{6}
\]

### Step 3: Solve for \(x\)

Since the denominators are the same, equate the numerators:

\[
x = 5
\]

### Final Answer:

\[
x = 5
\]

Would you like any further explanations or have any questions?

### Related Questions:
1. How do you solve rational equations with different denominators?
2. What are some common mistakes to avoid when solving rational equations?
3. How can you verify the solution of a rational equation?
4. What is the importance of finding the least common denominator in rational equations?
5. How do you handle rational equations with multiple variables?

**Tip:** Always check for extraneous solutions when solving rational equations by substituting back into the original equation.

Solve the rational equation: x/3 - x/6 = 5/6

Learn how to solve the rational equation x/3 - x/6 = 5/6 in three simple steps. This solution explains how to find the least common denominator, combine fractions, and solve for x. Perfect for students in Grades 7-9.

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