How to find limits algebraically

Now Playing:Finding limits algebraically when direct substitution is not possible– Example 1

Simplify Out "Zero Denominator" by Cancelling Common Factors
Find $\lim_{x \to 3} \;\frac{{{x^2} - 9}}{{x - 3}}$
Expand First, Then Simplify Out "Zero Denominator" by Cancelling Common Factors
Evaluate $\lim_{h \to 0} \;\frac{{{{\left( {5 + h} \right)}^2} - 25}}{h}$
Simplify Out "Zero Denominator" by Rationalizing Radicals
Evaluate:
1. $\lim_{x \to 4} \;\frac{{4 - x}}{{2 - \sqrt x }}$
  (hint: rationalize the denominator by multiplying its conjugate)
Find Limits of Functions involving Absolute Value
Evaluate $\lim_{x \to 0} \;\frac{{\left| x \right|}}{x}$
(hint: express the absolute value function as a piece-wise function)
Find Limits Using the Trigonometric Identity: $\lim_{\theta \to 0} \;\frac{{{sin\;}\theta}}{{\theta}}=1$
Find $\lim_{x \to 0} \;\frac{{{sin\;}5x}}{{2x}}$

Finding limits algebraically - when direct substitution is not possible