Evaluate ((m+3)/(m^2-16))/((m^2-9)/(m+4))

$\frac{\frac{m + 3}{m^{2} - 16}}{\frac{m^{2} - 9}{m + 4}}$

Step 1

Multiply the numerator by the reciprocal of the denominator.

$\frac{m + 3}{m^{2} - 16} \cdot \frac{m + 4}{m^{2} - 9}$

Step 2

Simplify the denominator.

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

$\frac{m + 3}{m^{2} - 4^{2}} \cdot \frac{m + 4}{m^{2} - 9}$

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

$\frac{m + 3}{(m + 4) (m - 4)} \cdot \frac{m + 4}{m^{2} - 9}$

Step 3

Simplify terms.

Cancel the common factor of $m + 4$ .

Cancel the common factor.

$\frac{m + 3}{(m + 4) (m - 4)} \cdot \frac{m + 4}{m^{2} - 9}$

Rewrite the expression.

$\frac{m + 3}{m - 4} \cdot \frac{1}{m^{2} - 9}$

Multiply $\frac{m + 3}{m - 4}$ by $\frac{1}{m^{2} - 9}$ .

$\frac{m + 3}{(m - 4) (m^{2} - 9)}$

Step 4

Simplify the denominator.

Rewrite $9$ as $3^{2}$ .

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

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = m$ and $b = 3$ .

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

Step 5

Cancel the common factor of $m + 3$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{(m - 4) (m - 3)}$