Simplify (3x+12)/(x^2-16)

$\frac{3 x + 12}{x^{2} - 16}$

Step 1

Factor $3$ out of $3 x + 12$ .

Factor $3$ out of $3 x$ .

$\frac{3 (x) + 12}{x^{2} - 16}$

Factor $3$ out of $12$ .

$\frac{3 x + 3 \cdot 4}{x^{2} - 16}$

Factor $3$ out of $3 x + 3 \cdot 4$ .

$\frac{3 (x + 4)}{x^{2} - 16}$

Step 2

Simplify the denominator.

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

$\frac{3 (x + 4)}{x^{2} - 4^{2}}$

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 $b = 4$ .

$\frac{3 (x + 4)}{(x + 4) (x - 4)}$

Step 3

Cancel the common factor of $x + 4$ .

Cancel the common factor.

$\frac{3 (x + 4)}{(x + 4) (x - 4)}$

Rewrite the expression.

$\frac{3}{x - 4}$