Simplify ((3x^2)/(x+2))÷((3x)/(x^2-4))

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

Step 1

To divide by a fraction, multiply by its reciprocal.

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

Step 2

Simplify terms.

Cancel the common factor of $3 x$ .

Factor $3 x$ out of $3 x^{2}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $\frac{x}{x + 2}$ by $x^{2} - 4$ .

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

Step 3

Simplify the numerator.

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

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

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 $b = 2$ .

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

Step 4

Simplify terms.

Cancel the common factor of $x + 2$ .

Cancel the common factor.

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

Divide $x (x - 2)$ by $1$ .

$x (x - 2)$

Apply the distributive property.

$x \cdot x + x \cdot - 2$

Simplify the expression.

Multiply $x$ by $x$ .

$x^{2} + x \cdot - 2$

Move $- 2$ to the left of $x$ .

$x^{2} - 2 x$