Divide ((x-2)/2)÷((x^2-4)/3)

$\frac{x - 2}{2} \div \frac{x^{2} - 4}{3}$

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Simplify the denominator.

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

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

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 $b = 2$ .

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

Step 3

Cancel the common factor of $x - 2$ .

Factor $x - 2$ out of $(x + 2) (x - 2)$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 4

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

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