Finding the Domain of a Rational Function

Find the domain of $f (x) = \frac{x + 3}{x^{2} - 9} .$

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
Begin by setting the denominator equal to zero and solving.

$\begin{matrix} x^{2} - 9 & = & 0 \\ x^{2} & = & 9 \\ x & = & ±3 \end{matrix}$
The denominator is equal to zero when $x = \pm 3.$ The domain of the function is all real numbers except $x = \pm 3.$

Your turn

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

Find the domain of $f (x) = \frac{4 x}{5 (x - 1) (x - 5)} .$

How did it go?