1. stuck on limits problem

evaluate the limit, if it exists:

lim x^2+x-6/x-2
→ 2

How do I go about solving this?

2. Originally Posted by DroMan
evaluate the limit, if it exists:

lim x^2+x-6/x-2
→ 2

How do I go about solving this?
factorize the numerator

cancel the denominator

take the limit

3. $\mathop {\lim }\limits_{x \to 2} \frac{{x^2 + x - 6}}
{{x - 2}} \hfill \\$

$= \mathop {\lim }\limits_{x \to 2} \frac{{\left( {x + 3} \right)\left( {x - 2} \right)}}
{{x - 2}} \hfill \\$

$= \mathop {\lim }\limits_{x \to 2} \left( {x + 3} \right) \hfill \\$

$= 2 + 3 \hfill \\$

$= 5 \hfill \\$