Question

2. (11 pts) Evaluate the following limits using the method of your choice. Show work to support your

Answer 1

2x - 6 = 2 (x - 3)

and

x² - 5x + 6 = (x - 3) (x - 2)

so that

$\displaystyle\lim_{x\to3}\frac{2x-6}{x^2-5x+6}=\lim_{x\to3}\frac2{x-2}=\boxed{2}$