Question

Please ans my question..​

Answer 1

$\sf \Large Solution!!$

$\sf \lim_{x\to 1}[\frac{x-2}{x^{2}-x}-\frac{1}{x^{3}-3x^{2}+2x}]$

$\sf \lim_{x\to 1}[\frac{x-2}{x(x-1)}-\frac{1}{x(x^{2}-3x+2)}]$

$\sf \lim_{x\to 1}[\frac{x-2}{x(x-1)}-\frac{1}{x(x^{2}-2x-x+2)}]$

$\sf \lim_{x\to 1}[\frac{x-2}{x(x-1)}-\frac{1}{x(x-2)(x-1)}]$

$\sf \lim_{x\to 1}[\frac{(x-2)^{2}-1}{x(x-2)(x-1)}]$

$\sf \lim_{x\to 1}[\frac{(x-2+1)(x-2-1)}{x(x-2)(x-1)}]$

$\sf \lim_{x\to 1}[\frac{\cancel{(x-1)}(x-3)}{x(x-2)\cancel{(x-1)}}]$

$\sf \lim_{x\to 1}\frac{x-3}{x(x-2)}$

$\sf \to \frac{1-3}{1(1-2)}$

$\sf \to \frac{\cancel -2}{\cancel -1}$

$\sf \to 2$