Precalculus Examples

Let $f (x) = x^{2} - 16$ and $g (x) = x + 4$ Find $\frac{f}{g}$ and its domain.

Step 1

Evaluate the numerator in $\frac{f}{g}$ .

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Step 1.1

Replace the function designators in $f$ with the actual functions.

$x^{2} - 16$

Step 1.2

Remove parentheses.

$x^{2} - 16$

Step 2

Evaluate the denominator in $\frac{f}{g}$ .

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Step 2.1

Replace the function designators in $g$ with the actual functions.

$x + 4$

Step 2.2

Remove parentheses.

$x + 4$

Step 3

Rewrite $\frac{f}{g}$ .

$\frac{x^{2} - 16}{x + 4}$

Step 4

Simplify $\frac{x^{2} - 16}{x + 4}$ .

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Step 4.1

Simplify the numerator.

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Step 4.1.1

Rewrite $16$ as $4^{2}$ .

$\frac{x^{2} - 4^{2}}{x + 4}$

Step 4.1.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x$ and $b = 4$ .

$\frac{(x + 4) (x - 4)}{x + 4}$

Step 4.2

Cancel the common factor of $x + 4$ .

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Step 4.2.1

Cancel the common factor.

$\frac{(x + 4) (x - 4)}{x + 4}$

Step 4.2.2

Divide $x - 4$ by $1$ .

$x - 4$