Answer:
The given function is [tex]y=\frac{\left(x^2-7x+12\right)}{x-3}[/tex]
factor the [tex]x^2-7x+12[/tex]
Re- write above as,
[tex]x^2-4x-3x+12[/tex]
[tex]x(x-4)-3(x-4)[/tex]
[tex](x-4)(x-3)[/tex]
The function as:
[tex]y=\frac{(x-4)(x-3)}{x-3}[/tex]
and simplifies to
f(x) = x -4 . . . . . . . . x ≠3
The graph is straight line y = x-4, with a hole at x=3.
The graph is shown in figure-1
