Find g(f(x)) f(x)=(x^2-36)/(x+6) , g(x)=x-6

$f (x) = \frac{x^{2} - 36}{x + 6}$ , $g (x) = x - 6$

Step 1

Set up the composite result function.

$g (f (x))$

Step 2

Evaluate $g (\frac{x^{2} - 36}{x + 6})$ by substituting in the value of $f$ into $g$ .

$g (\frac{x^{2} - 36}{x + 6}) = (\frac{x^{2} - 36}{x + 6}) - 6$

Step 3

Simplify each term.

Simplify the numerator.

Rewrite $36$ as $6^{2}$ .

$g (\frac{x^{2} - 36}{x + 6}) = \frac{x^{2} - 6^{2}}{x + 6} - 6$

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 $b = 6$ .

$g (\frac{x^{2} - 36}{x + 6}) = \frac{(x + 6) (x - 6)}{x + 6} - 6$

Cancel the common factor of $x + 6$ .

Cancel the common factor.

$g (\frac{x^{2} - 36}{x + 6}) = \frac{(x + 6) (x - 6)}{x + 6} - 6$

Divide $x - 6$ by $1$ .

$g (\frac{x^{2} - 36}{x + 6}) = x - 6 - 6$

Step 4

Subtract $6$ from $- 6$ .

$g (\frac{x^{2} - 36}{x + 6}) = x - 12$