Answer
The given statement makes sense.
Work Step by Step
We have to subtract $\frac{3x-5}{x-1}$ from $\frac{x-3}{x-1}$
And write the above statement in the form of a mathematical expression.
$\frac{x-3}{x-1}-\frac{3x-5}{x-1}$
Now, perform the subtraction of the rational algebraic expressions.
$\begin{align}
& \frac{x-3}{x-1}-\frac{3x-5}{x-1}=\frac{x-3-\left( 3x-5 \right)}{x-1} \\
& =\frac{x-3-3x+5}{x-1} \\
& =\frac{-2x+2}{x-1}
\end{align}$
And factorize the numerator by taking out a common factor and simplify.
$\begin{align}
& \frac{x-3}{x-1}-\frac{3x-5}{x-1}=\frac{-2\left( x-1 \right)}{\left( x-1 \right)} \\
& =-2
\end{align}$
Thus, the result of the given algebraic expression is a constant. Hence, the given statement makes sense.
