Let's simplify the given fraction step by step:
The expression we need to simplify is:
[tex]\[
\frac{x-1}{1-x}
\][/tex]
First, observe the relationship between the numerator and the denominator. Notice that the numerator, \(x-1\), and the denominator, \(1-x\), are closely related. Specifically:
[tex]\[
1 - x \text{ is actually } -(x - 1)
\][/tex]
This means:
[tex]\[
1 - x = - (x - 1)
\][/tex]
So, the given fraction can be rewritten as:
[tex]\[
\frac{x-1}{1-x} = \frac{x-1}{-(x-1)}
\][/tex]
Now, we can simplify this by factoring out the negative sign in the denominator:
[tex]\[
\frac{x-1}{-(x-1)} = -1
\][/tex]
Therefore, the simplified form of the given expression \(\frac{x-1}{1-x}\) is:
[tex]\[
-1
\][/tex]
The correct answer is A. [tex]\(-1\)[/tex].
