Question

$\underset{x\to 2}{\lim }\left(\frac{1}{x-2}-\frac{2}{x^2-2x}\right)$

Answer 1

$$\begin{gathered} \underset{x\to 2}{\lim }\left[\frac{1}{x-2}-\frac{2}{x^2-2x}\right] \\ =\underset{x\to 2}{\lim }\left[\frac{1}{x-2}-\frac{2}{x\left(x-2\right)}\right] \\ =\underset{x\to 2}{\lim }\left[\frac{x-2}{x\left(x-2\right)}\right] \\ =\underset{x\to 2}{\lim }\left[\frac{1}{x}\right] \\ =\frac{1}{2} \end{gathered}$$