Simplify (x+2)/(x^2-9)*(x+3)/(x^2-4)

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

Simplify the denominator.

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

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

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 $b = 3$ .

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

Simplify the denominator.

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

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

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 $b = 2$ .

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

Simplify terms.

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Rewrite the expression.

$\frac{1}{(x + 3) (x - 3)} \cdot \frac{x + 3}{x - 2}$

Cancel the common factor of $x + 3$ .

Cancel the common factor.

$\frac{1}{(x + 3) (x - 3)} \cdot \frac{x + 3}{x - 2}$

Rewrite the expression.

$\frac{1}{x - 3} \cdot \frac{1}{x - 2}$

Multiply $\frac{1}{x - 3}$ by $\frac{1}{x - 2}$ .

$\frac{1}{(x - 3) (x - 2)}$