To solve the equation \( \frac{3}{x-1} = \frac{2}{x-5} \), follow these steps:

1. **Cross-multiply** to eliminate the fractions:
   \[
   3(x - 5) = 2(x - 1)
   \]

2. **Distribute** the terms on both sides:
   \[
   3x - 15 = 2x - 2
   \]

3. **Isolate the variable \( x \)** by moving terms involving \( x \) to one side and the constants to the other:
   \[
   3x - 2x = -2 + 15
   \]
   \[
   x = 13
   \]

So, the solution is \( x = 13 \).

### Would you like details or have any questions?

Here are 5 related questions:
1. What is the general method to solve equations involving fractions?
2. Can equations like this have no solution? If so, how?
3. How would the solution change if the equation were \( \frac{3}{x+1} = \frac{2}{x+5} \)?
4. What are the potential pitfalls when cross-multiplying in equations?
5. How can you check if the solution is correct?

**Tip:** Always check if your solution is valid by substituting it back into the original equation to avoid extraneous solutions.

This guide walks you through solving the rational equation 3/(x-1) = 2/(x-5) with a step-by-step solution using cross-multiplication. Key algebraic concepts such as rational equations and properties of equality are covered. Suitable for students in Grades 8-10.

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