Question

Evaluate:

$\underset{x\to 2}{lim}\frac{x(x^2-4)}{x^2-5x+6}$

Answer 1

Now,

$\underset{x\to 2}{lim}\frac{x(x^2-4)}{x^2-5x+6}$

$=\underset{x\to 2}{lim}\frac{x(x-2)(x+2)}{(x-2)(x-3)}$

$=\underset{x\to 2}{lim}\frac{x(x+2)}{(x-3)}$

$=\frac{2\ast 4}{2-3}$

$=-8$.