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The solution to the equation \(\frac{x - 4}{x + 6} = \frac{3}{7}\) is \(x = 11.5\).

Would you like a detailed breakdown of the steps, or do you have any other questions?

Here are 5 related questions to expand your understanding:
1. What steps are involved in solving equations with fractions?
2. How can we verify the solution for this equation?
3. What happens if the denominator is zero in such equations?
4. How do you solve equations with multiple fractions on both sides?
5. What other methods could be used to solve this equation?

**Tip:** Always check for restrictions in the denominator when solving rational equations, as division by zero is undefined.

This lesson explains how to solve the rational equation (x - 4) / (x + 6) = 3 / 7 by using cross-multiplication and solving the resulting linear equation. Suitable for students in Grades 8-10.

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