Given the following rational expression, identify the simplified form below.x−55−x

1. Break Down the Problem

We need to simplify the rational expression $\frac{x - 5}{5 - x}$.

2. Relevant Concepts

To simplify a rational expression, we can factor out common terms and identify any relationships between the numerator and denominator. Specifically, note that $5 - x$ can be rewritten as $-(x - 5)$.

3. Analysis and Detail

Starting with the expression:

$\frac{x - 5}{5 - x}$

We can rewrite the denominator:

$5 - x = -(x - 5)$

Putting it back into the expression gives us:

$\frac{x - 5}{-(x - 5)} = -1 \text{ (for } x \neq 5\text{)}$

4. Verify and Summarize

The result is valid for all $x$ except $x = 5$, where the original expression is undefined.

Final Answer

The simplified form of the expression is $-1$ (for $x \neq 5$).