Algebra Examples

$f (x) = x + 5$ , $g (x) = \frac{9}{x^{2} - 25}$

Step 1

Set up the composite result function.

$f (g (x))$

Step 2

Evaluate $f (\frac{9}{x^{2} - 25})$ by substituting in the value of $g$ into $f$ .

$f (\frac{9}{x^{2} - 25}) = (\frac{9}{x^{2} - 25}) + 5$

Step 3

Simplify the denominator.

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Step 3.1

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

$f (\frac{9}{x^{2} - 25}) = \frac{9}{x^{2} - 5^{2}} + 5$

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 $a = x$ and $b = 5$ .

$f (\frac{9}{x^{2} - 25}) = \frac{9}{(x + 5) (x - 5)} + 5$