The given functions are
[tex]\begin{gathered} f(x)=2x-3 \\ g(x)=3x-6 \end{gathered}[/tex]Let's find the quotient between these functions
[tex]\frac{f(x)}{g(x)}=\frac{2x-3}{3x-6}[/tex]The domain of this new function is determined by the denominator 3x-6 because it can't be equal to zero.
[tex]3x-6\ne0[/tex]Let's solve for x
[tex]\begin{gathered} 3x-6\ne0 \\ 3x\ne6 \\ x\ne\frac{6}{3} \\ x\ne2 \end{gathered}[/tex]This means the domain must have a restriction.
In words, the domain of the function is all real numbers except the number 2.
