Answer
Please see below.
Work Step by Step
$$f(2.9) \approx -0.90909091 \\ f(2.99) \approx -0.99009901 \\ f(2.999) \approx -0.999001 \\ f(3)= \text{undefined} \\ f(3.001) \approx -1.001001 \\ f(3.01) \approx -1.010101 \\ f(3.1) \approx -1.1111111$$
So, we can estimate that$$\lim_{x \to 3}\frac{x-3}{x^2-7x+12}=-1,$$which is confirmed by the graph of the function
