Finding limits algebraically  when direct substitution is not possible
Finding limits algebraically  when direct substitution is not possible
There are times when applying direct substitution would only give us an undefined solution. In this section, we will explore some cool tricks to evaluate limits algebraically, such as using conjugates, trigonometry, common denominators, and factoring.
Lessons

3.
Simplify Out "Zero Denominator" by Rationalizing Radicals
Evaluate:

b)
$\lim_{x \to 7} \;\frac{{\sqrt {x + 2}  3}}{{x  7}}$ (hint: rationalize the numerator by multiplying its conjugate)