분수식 극한과 미정계수

$\displaystyle \lim\limits _{x \rightarrow 2} {} \frac{x ^{2} - x + a}{x - 2}$에서 $x \rightarrow 2$일 때, (분모)$\rightarrow$$0$이므로 (분자)$\rightarrow 0$이어야 한다. 즉, $\displaystyle \lim\limits _{x \rightarrow 2} {\left( x ^{2} - x + a \right)} = 0$, $2 + a = 0$, $a = - 2$ $\displaystyle \lim\limits _{x \rightarrow 2} {} \frac{x ^{2} - x + a}{x - 2}$$\displaystyle = \lim\limits _{x \rightarrow 2} {} \frac{x ^{2} - x - 2}{x - 2}$ $\displaystyle = \lim\limits _{x \rightarrow 2} {} \frac{\left( x - 2 \right) \left( x + 1 \right)}{x - 2} = 3$ $\therefore a + b = \left( - 2 \right) + 3 = 1$