Answer:
The correct option is D.
Step-by-step explanation:
The given functions are
[tex]f(x)=2x^2+x-3[/tex]
[tex]g(x)=x-1[/tex]
Both functions are polynomial and the domain of any polynomial is the set of all real numbers.
[tex](\frac{f}{g})x=\frac{f(x)}{g(x)}=\frac{2x^2+x-3}{x-1}[/tex]
[tex](\frac{f}{g})x=\frac{2x^2+3x-2x-3}{x-1}[/tex]
[tex](\frac{f}{g})x=\frac{x(2x+3)-1(2x+3)}{x-1}[/tex]
[tex](\frac{f}{g})x=\frac{(2x+3)(x-1)}{x-1}[/tex]
[tex](\frac{f}{g})x=2x+3[/tex]
The domain of [tex](\frac{f}{g})x[/tex] is all real number except x=1, because at x=1, g(x)=0.
Therefore option D is correct.
