Let's solve the equation \( \frac{10}{x} - 3 = \frac{7}{x} + 6 \).

### Step 1: Isolate the fractions
First, move all terms with \( x \) to one side and constants to the other side.

\[
\frac{10}{x} - \frac{7}{x} = 6 + 3
\]

Simplify both sides:

\[
\frac{10 - 7}{x} = 9
\]

\[
\frac{3}{x} = 9
\]

### Step 2: Solve for \( x \)
Multiply both sides by \( x \) to get rid of the fraction:

\[
3 = 9x
\]

Now, divide both sides by 9:

\[
x = \frac{3}{9} = \frac{1}{3}
\]

### Final Answer:
\[
x = \frac{1}{3}
\]

Would you like more details or have any other questions?

Here are 5 related questions to expand your understanding:

1. How do you solve equations with fractions that contain variables in both the numerator and denominator?
2. What happens if \( x = 0 \) in equations like \( \frac{a}{x} \)?
3. How do you handle equations with more complex denominators?
4. What are some common methods for solving rational equations?
5. How can you check if your solution is correct?

**Tip**: When solving equations with fractions, multiplying through by the least common denominator (LCD) helps eliminate the fractions early in the process!

This detailed guide walks you through solving the rational equation 10/x - 3 = 7/x + 6. Learn how to isolate variables, simplify fractions, and solve for x. Suitable for students in Grades 8-10, this problem covers key concepts in algebra and rational equations.

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