Evaluating the Limit of a Quotient by Factoring

Evaluate $\lim_{x \to 2} (\frac{x^{2} - 6 x + 8}{x - 2}) .$

Work it out on paper first. Then open the solution one step at a time, and stop as soon as you can finish on your own.

Solution
Factor where possible, and simplify.

$\begin{array}{l} \lim_{x \to 2} (\frac{x^{2} - 6 x + 8}{x - 2}) = \lim_{x \to 2} (\frac{(x - 2) (x - 4)}{x - 2}) & Factor the numerator . \\ = \lim_{x \to 2} (\frac{(x - 2) (x - 4)}{x - 2}) & Cancel the common factors . \\ = \lim_{x \to 2} (x - 4) & Evaluate . \\ = 2 - 4 = - 2 \end{array}$

Your turn

The book's Try It right after this example: same idea, new numbers. Only the answer is given.

Evaluate the following limit: $\lim_{x \to 7} (\frac{x^{2} - 11 x + 28}{7 - x}) .$

How did it go?