Answer
$\frac{x-1}{2x-3}$ where $x\ne\frac{3}{2}$
Work Step by Step
We are given that $f(x)=x-1$ and $g(x)=2x-3$. We know that $(\frac{f}{g})(x)=\frac{f(x)}{g(x)}$.
Therefore, $(\frac{f}{g})(x)=\frac{f(x)}{g(x)}=\frac{x-1}{2x-3}$.
However, the denominator cannot be equal to 0. Therefore, $2x-3\ne0$.
Add 3 to both sides.
$2x\ne3$
Divide both sides by 2.
$x\ne\frac{3}{2}$
