#### Answer

$\lim\limits_{x \to 2}\frac{(x^{2} - 7x +10)}{(x-2)} = \lim\limits_{x \to 2}(x-5) = -3$

#### Work Step by Step

Simplify:
$\frac{(x^{2} - 7x +10)}{(x-2)} = \frac{(x-5)(x-2)}{(x-2)} = (x-5)$
Now,
$\lim\limits_{x \to 2}\frac{(x^{2} - 7x +10)}{(x-2)} = \lim\limits_{x \to 2}(x-5) = -3$