Following the hint, we divide both the top and the bottom by x − 2 {\displaystyle x-2} to get
lim x → 2 x 2 − 3 x + 2 x − 2 = lim x → 2 ( x − 1 ) ( x − 2 ) x − 2 = lim x → 2 ( x − 1 ) = 2 − 1 = 1. {\displaystyle \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 1. {\displaystyle \color {blue}1.}
to get
