To simplify the expression $\frac{x-7}{7-x}$, we can first factor out a negative from the denominator to get:
$$\frac{x-7}{-(x-7)}$$
Then, we can cancel out the common factor of $(x-7)$ to get:
$$\frac{1}{-1}$$
Simplifying further, we get:
$$\boxed{-1}$$
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