The equation given is:

\[
\frac{2x - 5}{x + 4} = 1
\]

### Step 1: Eliminate the fraction
Multiply both sides by \( x + 4 \) to eliminate the fraction:

\[
(x + 4) \cdot \frac{2x - 5}{x + 4} = 1 \cdot (x + 4)
\]

Simplifying gives:

\[
2x - 5 = x + 4
\]

### Step 2: Solve for \( x \)
Now, subtract \( x \) from both sides to isolate \( x \):

\[
2x - x = 4 + 5
\]

Simplify:

\[
x = 9
\]

### Step 3: Check for extraneous solutions
We found \( x = 9 \). Now, we need to ensure there are no restrictions on \( x \) in the original equation.

The only restriction occurs if the denominator \( x + 4 = 0 \), which would happen when \( x = -4 \). Since \( x = 9 \) does not violate this condition, it is a valid solution.

### Final Answer
The only solution is \( \boxed{9} \).

If you need any further clarification, feel free to ask!

Here are some related questions that could be useful:

1. What are extraneous solutions, and how do they arise?
2. How do you solve rational equations with more complex fractions?
3. How can we solve equations with multiple solutions?
4. What are the steps to solve equations with radicals?
5. How do you solve equations with absolute value terms?

**Tip:** Always check for any values that might make the denominator zero, as these values must be excluded from the solution set.

Learn how to solve the rational equation (2x - 5) / (x + 4) = 1 step-by-step. This problem involves eliminating fractions, solving rational equations, and checking for extraneous solutions. Suitable for high school students in Grades 10-12.

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