Science:Math Exam Resources/Courses/MATH110/April 2016/Question 04 (b)/Solution 1

Following the hint, we divide both the top and the bottom by $x-2$ to get

$\lim _{x\to 2}{\frac {x^{2}-3x+2}{x-2}}=\lim _{x\to 2}{\frac {(x-1)(x-2)}{x-2}}=\lim _{x\to 2}(x-1)=2-1=1.$

Thus, the limit is $\color {blue}1.$