Question

lim x-2 [x-2/x^2-4-1/x^3-3x^2+x=​

Answer 1

$\star \: \: \: \underline {\sf{Solution :}}$

$\sf \lim_{x \to \: 2} \frac{x - 2}{ {x}^{2} - 4} - \frac{1}{ {x}^{3} - 3 {x}^{2} + x}$

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

$\implies \sf \lim_{x \to \: 2} \frac{{ \cancel{(x - 2)}}}{ \cancel{(x - 2)}(x + 2)} - \frac{1}{ {x}^{3} - 3 {x}^{2} + x}$

Putting value of limit

$\sf \implies \: \frac{1}{2 + 2} - \frac{1}{8 - 12 + 2}$

$\sf \implies \: \frac{3}{4}$