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

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

2. **Expand** both sides:
   \[
   2x - 4 = x + 1
   \]

3. **Move the terms involving \(x\)** to one side and the constants to the other side:
   \[
   2x - x = 1 + 4
   \]

4. **Simplify**:
   \[
   x = 5
   \]

So, the solution is \(x = 5\).

Would you like further details or have any questions? Here are five related questions:

1. How do you solve rational equations with different denominators?
2. What are the steps to cross-multiply when solving an equation?
3. How do you check if your solution is correct in a rational equation?
4. What happens if the equation has no solution?
5. Can there be more than one solution to a rational equation?

**Tip:** Always check for extraneous solutions, especially when dealing with rational equations. Plug the solution back into the original equation to verify it.

Learn how to solve the rational equation (x-2)/(x+1) = 1/2 with a step-by-step solution. This problem involves solving rational equations using cross-multiplication method. Suitable for students in Grades 9-12.

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