The problem states that the rational expression $\frac{3x-1}{1-3x}$ when simplified is equal to $-1$. We need to verify this.

1. Problem Description

The problem states that the rational expression $\frac{3x-1}{1-3x}$ when simplified is equal to $-1$. We need to verify this.

2. Solution Steps

We are given the rational expression $\frac{3x-1}{1-3x}$. We can factor out a $-1$ from the denominator to rewrite the expression.

$\frac{3x-1}{1-3x} = \frac{3x-1}{-(3x-1)}$

Now we can simplify the fraction by cancelling out the common factor of $(3x-1)$ in the numerator and denominator, provided that $3x-1 \ne 0$.

$\frac{3x-1}{-(3x-1)} = \frac{1}{-1} = -1$

However, we must consider the restriction $3x-1 \ne 0$, which means $3x \ne 1$, so $x \ne \frac{1}{3}$.

3. Final Answer

The given rational expression simplifies to $-1$ for $x \ne \frac{1}{3}$.