Question

$\underset{x\to 3}{\lim }\left(\frac{1}{x-3}-\frac{3}{x^2-3x}\right)$

Answer 1

$$\begin{gathered} \underset{x\to 3}{\lim }\left[\frac{1}{x-3}-\frac{3}{x^2-3x}\right] \\ =\underset{x\to 3}{\lim }\left[\frac{1}{x-3}-\frac{3}{x\left(x-3\right)}\right] \\ =\underset{x\to 3}{\lim }\left[\frac{x-3}{x\left(x-3\right)}\right] \\ =\underset{x\to 3}{\lim }\left[\frac{1}{x}\right] \\ =\frac{1}{3} \end{gathered}$$