Verify the Rational Expression: Is (-x+7)/(x-7) = 1 Correct?

To solve this problem, we'll follow these steps:

• Step 1: Simplify the equation $-x + 7 = x - 7$.
• Step 2: Solve for $x$ to verify if the equation holds true.

Now, let's work through each step:
Step 1: Starting with the equation $-x + 7 = x - 7$, we'll simplify by adding $x$ to both sides:
$-x + 7 + x = x - 7 + x$
This simplifies to $7 = 2x - 7$.
Next, add 7 to both sides to further simplify:
$7 + 7 = 2x - 7 + 7$
This gives $14 = 2x$.
Step 2: Divide both sides by 2 to solve for $x$:
$x = \frac{14}{2}$
Thus, $x = 7$.

However, substituting $x = 7$ into the original expression $\frac{-x + 7}{x - 7}$ results in division by zero, which is undefined. Therefore, $-x + 7$ cannot be equal to $x - 7$ for all values of $x$, and the simplification of the expression to 1 is incorrect under normal mathematical rules.

The simplification provided in the problem is incorrect.