Question

Examine the continuity of the function at $x=3$ defined as $f\left(x\right)=\frac{x^2-7x+12}{x^2-5x+6}$ for $x\ne 3$ and $x=3$

Answer 1

$f\left(x\right)=\frac{x^2-7x+12}{x^2-5x+6}=\frac{(x-3)(x-4)}{(x-3)(x-2)}$

For $x\ne 3,f\left(x\right)=\frac{x-4}{x-2}$

Since $f\left(x\right),x=3$ is not given we can not tell about continuity at $x=3$