Algebra Examples

$f (x) = \frac{9}{x^{2} - 25}$ , $g (x) = x + 8$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (x + 8)$ by substituting in the value of $g$ into $f$ .

$f (x + 8) = \frac{9}{{(x + 8)}^{2} - 25}$

Step 3

Simplify the denominator.

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Step 3.1

Rewrite $25$ as $5^{2}$ .

$f (x + 8) = \frac{9}{{(x + 8)}^{2} - 5^{2}}$

Step 3.2

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x + 8$ and $b = 5$ .

$f (x + 8) = \frac{9}{(x + 8 + 5) (x + 8 - 5)}$

Step 3.3

Simplify.

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Step 3.3.1

Add $8$ and $5$ .

$f (x + 8) = \frac{9}{(x + 13) (x + 8 - 5)}$

Step 3.3.2

Subtract $5$ from $8$ .

$f (x + 8) = \frac{9}{(x + 13) (x + 3)}$