Question

Solve:
$\underset{x\to 2}{lim}$ $(\frac{1}{x-2}-\frac{2}{x^2-2x})$

Answer 1

We have,

${lim}_{x\to 2}(\frac{1}{x-2}-\frac{2}{x^2-2x})$

${lim}_{x\to 2}(\frac{1}{x-2}-\frac{2}{x(x-2)})$

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

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

${lim}_{x\to 2}\left(\frac{1}{x}\right)$

$=\frac{1}{2}$

Hence, this is the answer.